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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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22 pages, 741 KiB  
Article
Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources
by Andrew Smith, Kanupriya Sinha and Christopher Jarzynski
Entropy 2022, 24(4), 474; https://doi.org/10.3390/e24040474 - 29 Mar 2022
Cited by 7 | Viewed by 5217
Abstract
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution [...] Read more.
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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18 pages, 2679 KiB  
Article
Entropy Generation during Head-On Interaction of Premixed Flames with Inert Walls within Turbulent Boundary Layers
by Sanjeev Kr. Ghai, Umair Ahmed, Nilanjan Chakraborty and Markus Klein
Entropy 2022, 24(4), 463; https://doi.org/10.3390/e24040463 - 27 Mar 2022
Cited by 8 | Viewed by 2128
Abstract
The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed [...] Read more.
The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed flame interaction with an isothermal wall is compared to that for an adiabatic wall. It has been found that entropy generation due to chemical reaction, thermal diffusion and molecular mixing remain comparable when the flame is away from the wall for both wall boundary conditions. However, the wall boundary condition affects the entropy generation during flame-wall interaction. In the case of isothermal wall, the entropy generation due to chemical reaction vanishes because of flame quenching and the entropy generation due to thermal diffusion becomes the leading entropy generator at the wall. By contrast, the entropy generation due to thermal diffusion and molecular mixing decrease at the adiabatic wall because of the vanishing wall-normal components of the gradients of temperature and species mass/mole fractions. These differences have significant effects on the overall entropy generation rate during flame-wall interaction, which suggest that combustor wall cooling needs to be optimized from the point of view of structural integrity and thermodynamic irreversibility. Full article
(This article belongs to the Special Issue Entropy Generation Analysis in Near-Wall Turbulent Flow)
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12 pages, 894 KiB  
Article
A Robust Protocol for Entropy Measurement in Mesoscopic Circuits
by Timothy Child, Owen Sheekey, Silvia Lüscher, Saeed Fallahi, Geoffrey C. Gardner, Michael Manfra and Joshua Folk
Entropy 2022, 24(3), 417; https://doi.org/10.3390/e24030417 - 17 Mar 2022
Cited by 13 | Viewed by 3444
Abstract
Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had [...] Read more.
Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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14 pages, 3369 KiB  
Article
A Multi-Classification Hybrid Quantum Neural Network Using an All-Qubit Multi-Observable Measurement Strategy
by Yi Zeng, Hao Wang, Jin He, Qijun Huang and Sheng Chang
Entropy 2022, 24(3), 394; https://doi.org/10.3390/e24030394 - 11 Mar 2022
Cited by 21 | Viewed by 5439
Abstract
Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the [...] Read more.
Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the number of qubits and the size of quantum circuits. In this paper, we propose a hybrid quantum neural network to implement multi-classification of a real-world dataset. We use an average pooling downsampling strategy to reduce the dimensionality of samples, and we design a ladder-like parameterized quantum circuit to disentangle the input states. Besides this, we adopt an all-qubit multi-observable measurement strategy to capture sufficient hidden information from the quantum system. The experimental results show that our algorithm outperforms the classical neural network and performs especially well on different multi-class datasets, which provides some enlightenment for the application of quantum computing to real-world data on near-term quantum processors. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing)
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16 pages, 1277 KiB  
Article
Information Field Theory and Artificial Intelligence
by Torsten Enßlin
Entropy 2022, 24(3), 374; https://doi.org/10.3390/e24030374 - 7 Mar 2022
Cited by 6 | Viewed by 3708
Abstract
Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems, including such for perception, cognition, and learning. This overlaps with IFT, [...] Read more.
Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems, including such for perception, cognition, and learning. This overlaps with IFT, which is designed to address perception, reasoning, and inference tasks. Here, the relation between concepts and tools in IFT and those in AI and ML research are discussed. In the context of IFT, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN) in ML. In this paper, the process of inference in IFT is reformulated in terms of GNN training. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture. Furthermore, the cross-fertilization of variational inference methods used in IFT and ML are discussed. These discussions suggest that IFT is well suited to address many problems in AI and ML research and application. Full article
(This article belongs to the Special Issue MaxEnt 2020/2021—The 40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)
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14 pages, 1209 KiB  
Article
Power-Optimal Control of a Stirling Engine’s Frictional Piston Motion
by Raphael Paul, Abdellah Khodja, Andreas Fischer, Robin Masser and Karl Heinz Hoffmann
Entropy 2022, 24(3), 362; https://doi.org/10.3390/e24030362 - 3 Mar 2022
Cited by 13 | Viewed by 2406
Abstract
The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular [...] Read more.
The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin’s maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method. Full article
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22 pages, 743 KiB  
Review
The Free Energy Principle for Perception and Action: A Deep Learning Perspective
by Pietro Mazzaglia, Tim Verbelen, Ozan Çatal and Bart Dhoedt
Entropy 2022, 24(2), 301; https://doi.org/10.3390/e24020301 - 21 Feb 2022
Cited by 57 | Viewed by 8751
Abstract
The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a [...] Read more.
The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a generative model of the world and plan actions in the future that will maintain the agent in an homeostatic state that satisfies its preferences. This framework lends itself to being realized in silico, as it comprehends important aspects that make it computationally affordable, such as variational inference and amortized planning. In this work, we investigate the tool of deep learning to design and realize artificial agents based on active inference, presenting a deep-learning oriented presentation of the free energy principle, surveying works that are relevant in both machine learning and active inference areas, and discussing the design choices that are involved in the implementation process. This manuscript probes newer perspectives for the active inference framework, grounding its theoretical aspects into more pragmatic affairs, offering a practical guide to active inference newcomers and a starting point for deep learning practitioners that would like to investigate implementations of the free energy principle. Full article
(This article belongs to the Special Issue Emerging Methods in Active Inference)
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15 pages, 9833 KiB  
Article
Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models
by Nina Megier, Andrea Smirne, Steve Campbell and Bassano Vacchini
Entropy 2022, 24(2), 304; https://doi.org/10.3390/e24020304 - 21 Feb 2022
Cited by 8 | Viewed by 2446
Abstract
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of [...] Read more.
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
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32 pages, 1028 KiB  
Review
Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
by Michael E. Cates, Étienne Fodor, Tomer Markovich, Cesare Nardini and Elsen Tjhung
Entropy 2022, 24(2), 254; https://doi.org/10.3390/e24020254 - 9 Feb 2022
Cited by 11 | Viewed by 2657
Abstract
Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in [...] Read more.
Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself. Full article
(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)
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27 pages, 883 KiB  
Article
Coupled Transport Effects in Solid Oxide Fuel Cell Modeling
by Aydan Gedik, Nico Lubos and Stephan Kabelac
Entropy 2022, 24(2), 224; https://doi.org/10.3390/e24020224 - 31 Jan 2022
Cited by 7 | Viewed by 3383
Abstract
With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are [...] Read more.
With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick’s law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring U,j-characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At T=1123.15 K and j=8000 A/m2, 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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32 pages, 1214 KiB  
Article
Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation
by Brian Joseph Edwards, Mohammad Hadi Nafar Sefiddashti and Bamin Khomami
Entropy 2022, 24(2), 175; https://doi.org/10.3390/e24020175 - 25 Jan 2022
Cited by 3 | Viewed by 3250
Abstract
The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption [...] Read more.
The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C1000H2002 polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory. Full article
(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)
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30 pages, 1722 KiB  
Article
Unraveling Hidden Major Factors by Breaking Heterogeneity into Homogeneous Parts within Many-System Problems
by Elizabeth P. Chou, Ting-Li Chen and Hsieh Fushing
Entropy 2022, 24(2), 170; https://doi.org/10.3390/e24020170 - 24 Jan 2022
Cited by 6 | Viewed by 2214
Abstract
For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, [...] Read more.
For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re–Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re–Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Anderson’s “More is Different” phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements—conditional mutual information and entropy—are heavily used in two selection criteria: C1—confirmable and C2—irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale. Full article
(This article belongs to the Special Issue Information Complexity in Structured Data)
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25 pages, 5419 KiB  
Article
Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index
by Nguyen Vo and Robert Ślepaczuk
Entropy 2022, 24(2), 158; https://doi.org/10.3390/e24020158 - 20 Jan 2022
Cited by 19 | Viewed by 5848
Abstract
This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data [...] Read more.
This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model. Full article
(This article belongs to the Special Issue Methods in Artificial Intelligence and Information Processing)
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14 pages, 821 KiB  
Article
Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks
by Robert Jankowski and Anna Chmiel
Entropy 2022, 24(1), 105; https://doi.org/10.3390/e24010105 - 9 Jan 2022
Cited by 7 | Viewed by 2469
Abstract
Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain [...] Read more.
Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain in one of five distinct states, resulting in the SIRQD model. The agent’s attitude towards respecting the restrictions of the pandemic plays a crucial role in its prevalence. In our model, the agent’s point of view could be altered by either conformism mechanism, social pressure, or independent actions. As the underlying opinion model, we leverage the q-voter model. The entire system constitutes a coupled opinion–dynamic model where two distinct processes occur. The question arises of how to properly align these dynamics, i.e., whether they should possess equal or disparate timescales. This paper highlights the impact of different timescales of opinion dynamics on epidemic spreading, focusing on the time and the infection’s peak. Full article
(This article belongs to the Special Issue Entropy and Social Physics)
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21 pages, 2718 KiB  
Article
Thermodynamic Rarity Assessment of Mobile Phone PCBs: A Physical Criticality Indicator in Times of Shortage
by Jorge Torrubia, Antonio Valero and Alicia Valero
Entropy 2022, 24(1), 100; https://doi.org/10.3390/e24010100 - 8 Jan 2022
Cited by 3 | Viewed by 1850
Abstract
Rising prices in energy, raw materials, and shortages of critical raw materials (CRMs) for renewable energies or electric vehicles are jeopardizing the transition to a low-carbon economy. Therefore, managing scarce resources must be a priority for governments. To that end, appropriate indicators that [...] Read more.
Rising prices in energy, raw materials, and shortages of critical raw materials (CRMs) for renewable energies or electric vehicles are jeopardizing the transition to a low-carbon economy. Therefore, managing scarce resources must be a priority for governments. To that end, appropriate indicators that can identify the criticality of raw materials and products is key. Thermodynamic rarity (TR) is an exergy-based indicator that measures the scarcity of elements in the earth’s crust and the energy intensity to extract and refine them. This paper uses TR to study 70 Mobile Phone (MP) Printed Circuit Boards (PCBs) samples. Results show that an average MP PCB has a TR of 88 MJ per unit, indicating their intensive use of valuable materials. Every year the embedded TR increases by 36,250 GWh worldwide -similar to the electricity consumed by Denmark in 2019- due to annual production of MP. Pd, Ta and Au embedded in MP PCBs worldwide between 2007 and 2021 contribute to 90% of the overall TR, which account for 75, 600 and 250 tones, respectively, and increasing by 11% annually. This, coupled with the short lifespan of MP, makes PCBs an important potential source of secondary resources. Full article
(This article belongs to the Section Thermodynamics)
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10 pages, 344 KiB  
Article
Permutation Entropy of Weakly Noise-Affected Signals
by Leonardo Ricci and Antonio Politi
Entropy 2022, 24(1), 54; https://doi.org/10.3390/e24010054 - 28 Dec 2021
Cited by 4 | Viewed by 1999
Abstract
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed [...] Read more.
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
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18 pages, 323 KiB  
Article
Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media
by Dick Bedeaux and Signe Kjelstrup
Entropy 2022, 24(1), 46; https://doi.org/10.3390/e24010046 - 27 Dec 2021
Cited by 12 | Viewed by 3024
Abstract
A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average [...] Read more.
A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed. Full article
(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)
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15 pages, 1233 KiB  
Article
Common Environmental Effects on Quantum Thermal Transistor
by Yu-Qiang Liu, Deng-Hui Yu and Chang-Shui Yu
Entropy 2022, 24(1), 32; https://doi.org/10.3390/e24010032 - 24 Dec 2021
Cited by 15 | Viewed by 2850
Abstract
Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three [...] Read more.
Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three strong-coupling qubits. It is shown that the functions of the thermal transistor can be maintained and the amplification rate can be modestly enhanced by the skillfully designed common environments. In particular, the presence of a dark state in the case of the completely correlated transitions can provide an additional external channel to control the heat currents without any disturbance of the amplification rate. These results show that common environmental effects can offer new insights into improving the performance of quantum thermal devices. Full article
(This article belongs to the Section Quantum Information)
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18 pages, 5484 KiB  
Article
Alternate Entropy Computations by Applying Recurrence Matrix Masking
by Charles L. Webber, Jr.
Entropy 2022, 24(1), 16; https://doi.org/10.3390/e24010016 - 23 Dec 2021
Cited by 4 | Viewed by 3305
Abstract
In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined [...] Read more.
In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed. Full article
(This article belongs to the Special Issue Complexity Science in Human Change: Research, Models, Clinical Applications)
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14 pages, 1409 KiB  
Article
MFF-Net: Deepfake Detection Network Based on Multi-Feature Fusion
by Lei Zhao, Mingcheng Zhang, Hongwei Ding and Xiaohui Cui
Entropy 2021, 23(12), 1692; https://doi.org/10.3390/e23121692 - 17 Dec 2021
Cited by 22 | Viewed by 4733
Abstract
Significant progress has been made in generating counterfeit images and videos. Forged videos generated by deepfaking have been widely spread and have caused severe societal impacts, which stir up public concern about automatic deepfake detection technology. Recently, many deepfake detection methods based on [...] Read more.
Significant progress has been made in generating counterfeit images and videos. Forged videos generated by deepfaking have been widely spread and have caused severe societal impacts, which stir up public concern about automatic deepfake detection technology. Recently, many deepfake detection methods based on forged features have been proposed. Among the popular forged features, textural features are widely used. However, most of the current texture-based detection methods extract textures directly from RGB images, ignoring the mature spectral analysis methods. Therefore, this research proposes a deepfake detection network fusing RGB features and textural information extracted by neural networks and signal processing methods, namely, MFF-Net. Specifically, it consists of four key components: (1) a feature extraction module to further extract textural and frequency information using the Gabor convolution and residual attention blocks; (2) a texture enhancement module to zoom into the subtle textural features in shallow layers; (3) an attention module to force the classifier to focus on the forged part; (4) two instances of feature fusion to firstly fuse textural features from the shallow RGB branch and feature extraction module and then to fuse the textural features and semantic information. Moreover, we further introduce a new diversity loss to force the feature extraction module to learn features of different scales and directions. The experimental results show that MFF-Net has excellent generalization and has achieved state-of-the-art performance on various deepfake datasets. Full article
(This article belongs to the Topic Machine and Deep Learning)
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21 pages, 799 KiB  
Article
The Influence of the Symmetry of Identical Particles on Flight Times
by Salvador Miret-Artés, Randall S. Dumont, Tom Rivlin and Eli Pollak
Entropy 2021, 23(12), 1675; https://doi.org/10.3390/e23121675 - 13 Dec 2021
Cited by 6 | Viewed by 2477
Abstract
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we [...] Read more.
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a ‘screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations II)
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25 pages, 5936 KiB  
Article
Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems
by Ali Mohammad-Djafari
Entropy 2021, 23(12), 1673; https://doi.org/10.3390/e23121673 - 13 Dec 2021
Cited by 19 | Viewed by 5234
Abstract
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of [...] Read more.
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion. Full article
(This article belongs to the Special Issue MaxEnt 2020/2021—The 40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)
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11 pages, 2062 KiB  
Article
Stochastic Collisional Quantum Thermometry
by Eoin O’Connor, Bassano Vacchini and Steve Campbell
Entropy 2021, 23(12), 1634; https://doi.org/10.3390/e23121634 - 6 Dec 2021
Cited by 11 | Viewed by 3084
Abstract
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage [...] Read more.
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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12 pages, 3626 KiB  
Article
Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics
by Samuel A. Cushman
Entropy 2021, 23(12), 1616; https://doi.org/10.3390/e23121616 - 1 Dec 2021
Cited by 8 | Viewed by 2714
Abstract
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds [...] Read more.
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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36 pages, 1647 KiB  
Article
Real-World Data Difficulty Estimation with the Use of Entropy
by Przemysław Juszczuk, Jan Kozak, Grzegorz Dziczkowski, Szymon Głowania, Tomasz Jach and Barbara Probierz
Entropy 2021, 23(12), 1621; https://doi.org/10.3390/e23121621 - 1 Dec 2021
Cited by 12 | Viewed by 3810
Abstract
In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information [...] Read more.
In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared. Full article
(This article belongs to the Special Issue Entropy in Real-World Datasets and Its Impact on Machine Learning)
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24 pages, 558 KiB  
Article
Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion
by Jin-Fu Chen, Tian Qiu and Hai-Tao Quan
Entropy 2021, 23(12), 1602; https://doi.org/10.3390/e23121602 - 29 Nov 2021
Cited by 12 | Viewed by 2251
Abstract
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of [...] Read more.
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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26 pages, 6435 KiB  
Article
A Hybrid Multi-Criteria Decision-Making Approach Based on ANP-Entropy TOPSIS for Building Materials Supplier Selection
by Chun-Ho Chen
Entropy 2021, 23(12), 1597; https://doi.org/10.3390/e23121597 - 28 Nov 2021
Cited by 36 | Viewed by 4071
Abstract
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained [...] Read more.
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained by constructing an evaluation matrix of the information based on the actual information of the evaluation criteria of the scheme, and obtained through multi-step calculations. Different decision-making methods are based on different weight types. Considering only one of the two weights often leads to biased results. In addition, in order to establish an effective supply chain, buyers must find suitable merchants among suppliers that provide quality products and/or services. Based on the above factors, it is difficult to choose a suitable alternative. The main contribution of this paper is to combine analytic network process (ANP), entropy weight and the technique for order preference by similarity to an ideal solution (TOPSIS) to construct a suitable multi-criteria decision (MCDM) model. By means of ANP-entropy weights to extend the TOPSIS method, ANP-entropy weights are used to replace subjective weights. A supplier selection decision-making model based on ANP-entropy TOPSIS is proposed. At last, the sensitivity analysis shows that, taking the selection of building materials suppliers as an example, the hybrid ANP-entropy TOPSIS method can effectively select suitable suppliers. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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32 pages, 1035 KiB  
Review
Quantum Transport of Particles and Entropy
by Christoph Strunk
Entropy 2021, 23(12), 1573; https://doi.org/10.3390/e23121573 - 25 Nov 2021
Cited by 5 | Viewed by 2934
Abstract
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric [...] Read more.
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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23 pages, 379 KiB  
Article
On Epistemics in Expected Free Energy for Linear Gaussian State Space Models
by Magnus T. Koudahl, Wouter M. Kouw and Bert de Vries
Entropy 2021, 23(12), 1565; https://doi.org/10.3390/e23121565 - 24 Nov 2021
Cited by 4 | Viewed by 2368
Abstract
Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a [...] Read more.
Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive. Full article
(This article belongs to the Special Issue Emerging Methods in Active Inference)
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19 pages, 1081 KiB  
Article
Cooling Cycle Optimization for a Vuilleumier Refrigerator
by Raphael Paul, Abdellah Khodja, Andreas Fischer and Karl Heinz Hoffmann
Entropy 2021, 23(12), 1562; https://doi.org/10.3390/e23121562 - 24 Nov 2021
Cited by 7 | Viewed by 1692
Abstract
Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity [...] Read more.
Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We find improvements of the cooling power of more than 15%. Full article
(This article belongs to the Section Thermodynamics)
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17 pages, 1446 KiB  
Article
A Quantum Blind Multi-Signature Method for the Industrial Blockchain
by Zhengying Cai, Shi Liu, Zhangyi Han, Rui Wang and Yuehua Huang
Entropy 2021, 23(11), 1520; https://doi.org/10.3390/e23111520 - 15 Nov 2021
Cited by 10 | Viewed by 2398
Abstract
Traditional anti-quantum methods and multi-signature technologies to secure the blockchain against quantum attacks will quickly reduce the efficiency and scalability of the industrial blockchain, where the computational resources will experience a polynomial rise with the increasing number of traders. Here, a quantum blind [...] Read more.
Traditional anti-quantum methods and multi-signature technologies to secure the blockchain against quantum attacks will quickly reduce the efficiency and scalability of the industrial blockchain, where the computational resources will experience a polynomial rise with the increasing number of traders. Here, a quantum blind multi-signature method is proposed for the multi-party transaction to provide anti-quantum security. First, the proposed multi-party transaction frame and quantum key distribution in the industrial blockchain are introduced. It integrates a novel quantum blind multi-signature algorithm that is based on the quantum entanglement mechanism, and it is absolutely secure in theory. Second, the anti-quantum multi-signature algorithm is illustrated, where there are four phases, i.e., initialization, signing, verification, and implementation. Third, the security and complexity of the proposed framework are analyzed and compared with related methods in references, and our proposed method is verified to be able to offer good computational performance and blockchain scalability for multi-party transaction. Last, the paper is summarized and future research directions are proposed. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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20 pages, 692 KiB  
Article
Thermality versus Objectivity: Can They Peacefully Coexist?
by Thao P. Le, Andreas Winter and Gerardo Adesso
Entropy 2021, 23(11), 1506; https://doi.org/10.3390/e23111506 - 13 Nov 2021
Cited by 8 | Viewed by 2634
Abstract
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum [...] Read more.
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical information that could conflict with thermalisation. Here, we examine the overlap between thermal and objective states. We find that in general, one cannot exist when the other is present. However, there are certain regimes where thermality and objectivity are more likely to coexist: in the high temperature limit, at the non-degenerate low temperature limit, and when the environment is large. This is consistent with our experiences that everyday-sized objects can be both thermal and objective. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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13 pages, 1108 KiB  
Article
Environment-Assisted Shortcuts to Adiabaticity
by Akram Touil and Sebastian Deffner
Entropy 2021, 23(11), 1479; https://doi.org/10.3390/e23111479 - 9 Nov 2021
Cited by 5 | Viewed by 2855
Abstract
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. [...] Read more.
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As the main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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33 pages, 1495 KiB  
Article
Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison
by Massimiliano Zanin and David Papo
Entropy 2021, 23(11), 1474; https://doi.org/10.3390/e23111474 - 8 Nov 2021
Cited by 20 | Viewed by 3551
Abstract
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, [...] Read more.
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues. Full article
(This article belongs to the Special Issue Entropy and Irreversibility in Biological Systems)
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37 pages, 2536 KiB  
Article
Taming the Chaos in Neural Network Time Series Predictions
by Sebastian Raubitzek and Thomas Neubauer
Entropy 2021, 23(11), 1424; https://doi.org/10.3390/e23111424 - 28 Oct 2021
Cited by 6 | Viewed by 2799
Abstract
Machine learning methods, such as Long Short-Term Memory (LSTM) neural networks can predict real-life time series data. Here, we present a new approach to predict time series data combining interpolation techniques, randomly parameterized LSTM neural networks and measures of signal complexity, which we [...] Read more.
Machine learning methods, such as Long Short-Term Memory (LSTM) neural networks can predict real-life time series data. Here, we present a new approach to predict time series data combining interpolation techniques, randomly parameterized LSTM neural networks and measures of signal complexity, which we will refer to as complexity measures throughout this research. First, we interpolate the time series data under study. Next, we predict the time series data using an ensemble of randomly parameterized LSTM neural networks. Finally, we filter the ensemble prediction based on the original data complexity to improve the predictability, i.e., we keep only predictions with a complexity close to that of the training data. We test the proposed approach on five different univariate time series data. We use linear and fractal interpolation to increase the amount of data. We tested five different complexity measures for the ensemble filters for time series data, i.e., the Hurst exponent, Shannon’s entropy, Fisher’s information, SVD entropy, and the spectrum of Lyapunov exponents. Our results show that the interpolated predictions consistently outperformed the non-interpolated ones. The best ensemble predictions always beat a baseline prediction based on a neural network with only a single hidden LSTM, gated recurrent unit (GRU) or simple recurrent neural network (RNN) layer. The complexity filters can reduce the error of a random ensemble prediction by a factor of 10. Further, because we use randomly parameterized neural networks, no hyperparameter tuning is required. We prove this method useful for real-time time series prediction because the optimization of hyperparameters, which is usually very costly and time-intensive, can be circumvented with the presented approach. Full article
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13 pages, 1199 KiB  
Article
Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels
by Katarzyna Siudzińska, Arpan Das and Anindita Bera
Entropy 2021, 23(11), 1382; https://doi.org/10.3390/e23111382 - 21 Oct 2021
Cited by 5 | Viewed by 1744
Abstract
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian [...] Read more.
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
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30 pages, 9881 KiB  
Review
Recent Advances in Loop Heat Pipes with Flat Evaporator
by Pawel Szymanski, Richard Law, Ryan J. MᶜGlen and David A. Reay
Entropy 2021, 23(11), 1374; https://doi.org/10.3390/e23111374 - 20 Oct 2021
Cited by 12 | Viewed by 4372
Abstract
The focus of this review is to present the current advances in Loop Heat Pipes (LHP) with flat evaporators, which address the current challenges to the wide implementation of the technology. A recent advance in LHP is the design of flat-shaped evaporators, which [...] Read more.
The focus of this review is to present the current advances in Loop Heat Pipes (LHP) with flat evaporators, which address the current challenges to the wide implementation of the technology. A recent advance in LHP is the design of flat-shaped evaporators, which is better suited to the geometry of discretely mounted electronics components (microprocessors) and therefore negate the need for an additional transfer surface (saddle) between component and evaporator. However, various challenges exist in the implementation of flat-evaporator, including (1) deformation of the evaporator due to high internal pressure and uneven stress distribution in the non-circular casing; (2) heat leak from evaporator heating zone and sidewall into the compensation chamber; (3) poor performance at start-up; (4) reverse flow through the wick; or (5) difficulties in sealing, and hence frequent leakage. This paper presents and reviews state-of-the-art LHP technologies; this includes an (a) review of novel manufacturing methods; (b) LHP evaporator designs; (c) working fluids; and (d) construction materials. The work presents solutions that are used to develop or improve the LHP construction, overall thermal performance, heat transfer distance, start-up time (especially at low heat loads), manufacturing cost, weight, possibilities of miniaturization and how they affect the solution on the above-presented problems and challenges in flat shape LHP development to take advantage in the passive cooling systems for electronic devices in multiple applications. Full article
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13 pages, 11972 KiB  
Article
Quantum Probes for the Characterization of Nonlinear Media
by Alessandro Candeloro, Sholeh Razavian, Matteo Piccolini, Berihu Teklu, Stefano Olivares and Matteo G. A. Paris
Entropy 2021, 23(10), 1353; https://doi.org/10.3390/e23101353 - 16 Oct 2021
Cited by 20 | Viewed by 2426
Abstract
Active optical media leading to interaction Hamiltonians of the form H=λ˜(a+a†)ζ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, [...] Read more.
Active optical media leading to interaction Hamiltonians of the form H=λ˜(a+a†)ζ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, as opposed to semiclassical ones. In particular, we investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling λ˜ and of the nonlinearity order ζ. Upon using tools from quantum estimation, we show that: (i) the two parameters are compatible, i.e., the may be jointly estimated without additional quantum noise; (ii) the use of squeezed probes improves precision at fixed overall energy of the probe; (iii) for low energy probes, squeezed vacuum represent the most convenient choice, whereas for increasing energy an optimal squeezing fraction may be determined; (iv) using optimized quantum probes, the scaling of the corresponding precision with energy improves, both for individual and joint estimation of the two parameters, compared to semiclassical coherent probes. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology. Full article
(This article belongs to the Special Issue Quantum Communication)
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36 pages, 7298 KiB  
Review
A Unified Treatment of Tribo-Components Degradation Using Thermodynamics Framework: A Review on Adhesive Wear
by Lijesh Koottaparambil and M. M. Khonsari
Entropy 2021, 23(10), 1329; https://doi.org/10.3390/e23101329 - 12 Oct 2021
Cited by 4 | Viewed by 2865
Abstract
An extensive survey of open literature reveals the need for a unifying approach for characterizing the degradation of tribo-pairs. This paper focuses on recent efforts made towards developing unified relationships for adhesive-type wear under unlubricated conditions through a thermodynamic framework. It is shown [...] Read more.
An extensive survey of open literature reveals the need for a unifying approach for characterizing the degradation of tribo-pairs. This paper focuses on recent efforts made towards developing unified relationships for adhesive-type wear under unlubricated conditions through a thermodynamic framework. It is shown that this framework can properly characterize many complex scenarios, such as degradation problems involving unidirectional, bidirectional (oscillatory and reciprocating motions), transient operating conditions (e.g., during the running-in period), and variable loading/speed sequencing. Full article
(This article belongs to the Section Entropy Reviews)
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11 pages, 279 KiB  
Article
The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation
by Wei Liu and Yong Zhang
Entropy 2021, 23(10), 1313; https://doi.org/10.3390/e23101313 - 7 Oct 2021
Cited by 13 | Viewed by 1764
Abstract
In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity. Full article
21 pages, 1221 KiB  
Article
Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure
by Xuewen Yu and Jim Q. Smith
Entropy 2021, 23(10), 1308; https://doi.org/10.3390/e23101308 - 6 Oct 2021
Cited by 6 | Viewed by 2021
Abstract
Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a [...] Read more.
Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a Bayesian network (BN). However, certain causal constructions that are particularly pertinent to the study of reliability are difficult to express fully through a BN. Our recent work demonstrated the flexibility of using a Chain Event Graph (CEG) instead to capture causal reasoning embedded within engineers’ reports. We demonstrated that an event tree rather than a BN could provide an alternative framework that could capture most of the causal concepts needed within this domain. In particular, a causal calculus for a specific type of intervention, called a remedial intervention, was devised on this tree-like graph. In this paper, we extend the use of this framework to show that not only remedial maintenance interventions but also interventions associated with routine maintenance can be well-defined using this alternative class of graphical model. We also show that the complexity in making inference about the potential relationships between causes and failures in a missing data situation in the domain of system reliability can be elegantly addressed using this new methodology. Causal modelling using a CEG is illustrated through examples drawn from the study of reliability of an energy distribution network. Full article
(This article belongs to the Special Issue Causal Inference for Heterogeneous Data and Information Theory)
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19 pages, 22390 KiB  
Article
Optimal Heat Exchanger Area Distribution and Low-Temperature Heat Sink Temperature for Power Optimization of an Endoreversible Space Carnot Cycle
by Tan Wang, Yanlin Ge, Lingen Chen, Huijun Feng and Jiuyang Yu
Entropy 2021, 23(10), 1285; https://doi.org/10.3390/e23101285 - 30 Sep 2021
Cited by 9 | Viewed by 1606
Abstract
Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the [...] Read more.
Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the optimization objective, the surface area distributions of three heat exchangers are optimized, and the maximum power output is obtained when the total heat transfer area of the three heat exchangers of the whole plant is fixed. Furthermore, the double-maximum power output is obtained by optimizing the temperature of a low-temperature heat sink. Finally, the influences of fixed plant parameters on the maximum power output performance are analyzed. The results show that there is an optimal temperature of the low-temperature heat sink and a couple of optimal area distributions that allow one to obtain the double-maximum power output. The results obtained have some guidelines for the design and optimization of actual space power plants. Full article
(This article belongs to the Section Thermodynamics)
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22 pages, 930 KiB  
Article
Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole
by Abdul Jawad, Shahid Chaudhary and Kazuharu Bamba
Entropy 2021, 23(10), 1269; https://doi.org/10.3390/e23101269 - 28 Sep 2021
Cited by 6 | Viewed by 1788
Abstract
We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, [...] Read more.
We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)
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33 pages, 4557 KiB  
Article
Stochastic Chaos and Markov Blankets
by Karl Friston, Conor Heins, Kai Ueltzhöffer, Lancelot Da Costa and Thomas Parr
Entropy 2021, 23(9), 1220; https://doi.org/10.3390/e23091220 - 17 Sep 2021
Cited by 69 | Viewed by 7846
Abstract
In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions [...] Read more.
In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems)
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14 pages, 881 KiB  
Article
Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics
by Dmitri Sokolovski and Alexandre Matzkin
Entropy 2021, 23(9), 1186; https://doi.org/10.3390/e23091186 - 9 Sep 2021
Cited by 3 | Viewed by 2257
Abstract
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two [...] Read more.
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations II)
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18 pages, 1105 KiB  
Article
Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
by Mariana Krasnytska, Bertrand Berche, Yurij Holovatch and Ralph Kenna
Entropy 2021, 23(9), 1175; https://doi.org/10.3390/e23091175 - 7 Sep 2021
Cited by 8 | Viewed by 4578
Abstract
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ [...] Read more.
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes. Full article
(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)
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30 pages, 6086 KiB  
Review
Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons
by Huiting Chen, Shiyu Wei, Weitian Ding, Han Wei, Liang Li, Henrik Saxén, Hongming Long and Yaowei Yu
Entropy 2021, 23(9), 1106; https://doi.org/10.3390/e23091106 - 25 Aug 2021
Cited by 12 | Viewed by 4173
Abstract
Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble [...] Read more.
Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted. Full article
(This article belongs to the Special Issue Entropy in Particle Systems)
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13 pages, 314 KiB  
Article
Quantum and Classical Ergotropy from Relative Entropies
by Akira Sone and Sebastian Deffner
Entropy 2021, 23(9), 1107; https://doi.org/10.3390/e23091107 - 25 Aug 2021
Cited by 16 | Viewed by 3949
Abstract
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect [...] Read more.
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
21 pages, 361 KiB  
Article
Generalized Ordinal Patterns and the KS-Entropy
by Tim Gutjahr and Karsten Keller
Entropy 2021, 23(8), 1097; https://doi.org/10.3390/e23081097 - 23 Aug 2021
Cited by 3 | Viewed by 2655
Abstract
Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based [...] Read more.
Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based on the probability distributions of such patterns is equal to Kolmogorov–Sinai entropy in simple one-dimensional systems. The general reason for this is that, roughly speaking, the system of ordinal patterns obtained for a real-valued “measuring arrangement” has high potential for separating orbits. Starting from a slightly different approach of A. Antoniouk, K. Keller and S. Maksymenko, we discuss the generalizations of ordinal patterns providing enough separation to determine the Kolmogorov–Sinai entropy. For defining these generalized ordinal patterns, the idea is to substitute the basic binary relation ≤ on the real numbers by another binary relation. Generalizing the former results of I. Stolz and K. Keller, we establish conditions that the binary relation and the dynamical system have to fulfill so that the obtained generalized ordinal patterns can be used for estimating the Kolmogorov–Sinai entropy. Full article
(This article belongs to the Special Issue Entropy Measures for Data Analysis II: Theory, Algorithms and Applications)
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18 pages, 1675 KiB  
Article
Some Interesting Observations on the Free Energy Principle
by Karl J. Friston, Lancelot Da Costa and Thomas Parr
Entropy 2021, 23(8), 1076; https://doi.org/10.3390/e23081076 - 19 Aug 2021
Cited by 49 | Viewed by 5947
Abstract
Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various [...] Read more.
Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket—and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics. Full article
(This article belongs to the Section Entropy and Biology)
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