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Entropy
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Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II
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Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Non-equilibrium Phenomena".

Deadline for manuscript submissions: closed (15 November 2024) | Viewed by 8281

Special Issue Editor

Dr. Eun-jin Kim

E-Mail Website
Guest Editor
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
Interests: fluid dynamics; magnetohydrodynamics (MHD); plasma physics; self-organisation; non-equilibrium statistical mechanics; turbulence; solar/stellar physics; magnetic fusion; information theory; homeostasis in biosystems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the improvements in high-resolution data, fluctuations have emerged universally, playing a crucial role in many disciplines. Some fluctuations, such as tornados, stock market crashes, and eruptions in laboratory/astrophysical plasmas, are of a large amplitude and can have a significant impact even if they occur rarely. These large fluctuations are part of the very nature of non-equilibrium systems.

Associated with fluctuations is randomness in the statistical sense or dissipation in the thermodynamic sense. The concept of entropy has been used to quantify such fluctuations, constituting one of the cornerstone concepts in thermodynamic equilibrium. However, entropy in the conventional form has a limited utility in helping us to understand non-equilibrium systems. In particular, the information geometric method has emerged as a useful tool to help us to understand fluctuations in non-equilibrium systems.

This Special Issue aims to present different approaches to the description of fluctuations in non-equilibrium systems based on entropy and its variants (mutual entropy, relative entropy, etc.), as well as information geometry.

Dr. Eun-jin Kim
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fluctuations
  • non-equilibrium
  • entropy
  • information geometry
  • dissipation
  • irreversibility
  • relative entropy
  • mutual entropy
  • generalized entropy
  • q-entropy
  • fractional calculus
  • intermittency
  • phase transition
  • patten formation
  • large deviation
  • self-assembly
  • hysteresis
  • generalized statistical mechanics
  • quantum systems
  • field theory
  • emergent phenomena
  • temperature

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Published Papers (4 papers)

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Research

17 pages, 3321 KiB  
Article
Sensitivity Analysis of Excited-State Population in Plasma Based on Relative Entropy
by Yosuke Shimada and Hiroshi Akatsuka
Entropy 2024, 26(9), 782; https://doi.org/10.3390/e26090782 - 12 Sep 2024
Viewed by 958
Abstract
A highly versatile evaluation method is proposed for transient plasmas based on statistical physics. It would be beneficial in various industrial sectors, including semiconductors and automobiles. Our research focused on low-energy plasmas in laboratory settings, and they were assessed via our proposed method, [...] Read more.
A highly versatile evaluation method is proposed for transient plasmas based on statistical physics. It would be beneficial in various industrial sectors, including semiconductors and automobiles. Our research focused on low-energy plasmas in laboratory settings, and they were assessed via our proposed method, which incorporates relative entropy and fractional Brownian motion, based on a revised collisional–radiative model. By introducing an indicator to evaluate how far a system is from its steady state, both the trend of entropy and the radiative process’ contribution to the lifetime of excited states were considered. The high statistical weight of some excited states may act as a bottleneck in the plasma’s energy relaxation throughout the system to a steady state. By deepening our understanding of how energy flows through plasmas, we anticipate potential contributions to resolving global environmental issues and fostering technological innovation in plasma-related industrial fields. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II)
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17 pages, 345 KiB  
Article
How to Partition a Quantum Observable
by Caleb Merrick Webb and Charles Allen Stafford
Entropy 2024, 26(7), 611; https://doi.org/10.3390/e26070611 - 20 Jul 2024
Cited by 1 | Viewed by 1014
Abstract
We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, [...] Read more.
We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy that is consistent with the laws of thermodynamics. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II)
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21 pages, 1514 KiB  
Article
Minimum Information Variability in Linear Langevin Systems via Model Predictive Control
by Adrian-Josue Guel-Cortez, Eun-jin Kim and Mohamed W. Mehrez
Entropy 2024, 26(4), 323; https://doi.org/10.3390/e26040323 - 10 Apr 2024
Viewed by 1492
Abstract
Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the [...] Read more.
Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum “geometric information variability”. We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II)
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23 pages, 4268 KiB  
Article
A Variational Synthesis of Evolutionary and Developmental Dynamics
by Karl Friston, Daniel A. Friedman, Axel Constant, V. Bleu Knight, Chris Fields, Thomas Parr and John O. Campbell
Entropy 2023, 25(7), 964; https://doi.org/10.3390/e25070964 - 21 Jun 2023
Cited by 13 | Viewed by 3973
Abstract
This paper introduces a variational formulation of natural selection, paying special attention to the nature of ‘things’ and the way that different ‘kinds’ of ‘things’ are individuated from—and influence—each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic [...] Read more.
This paper introduces a variational formulation of natural selection, paying special attention to the nature of ‘things’ and the way that different ‘kinds’ of ‘things’ are individuated from—and influence—each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain—and are constrained by—fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (Bayesian model) selection. The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations of distinct natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses—and identify points of contact with related mathematical formulations of evolution. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems II)
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