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8 pages, 256 KiB

Open AccessArticle

Fluctuating Diffusivity of RNA-Protein Particles: Analogy with Thermodynamics

by Yuichi Itto

Entropy 2021, 23(3), 333; https://doi.org/10.3390/e23030333 - 12 Mar 2021

Cited by 2 | Viewed by 2196

Abstract

A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs [...] Read more.

A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs of the quantity of heat and work are identified. The Clausius-like inequality is shown to hold for the entropy associated with diffusivity fluctuations, which plays a role analogous to the thermodynamic entropy, and the analog of the quantity of heat. The change of the statistical fluctuation distribution is also examined from a geometric perspective. The present discussions may contribute to a deeper understanding of the fluctuating diffusivity in view of the laws of thermodynamics. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

14 pages, 702 KiB

Open AccessArticle

Transient Dynamics in the Random Growth and Reset Model

by Tamás S. Biró, Lehel Csillag and Zoltán Néda

Entropy 2021, 23(3), 306; https://doi.org/10.3390/e23030306 - 5 Mar 2021

Cited by 8 | Viewed by 2443

Abstract

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes [...] Read more.

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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24 pages, 978 KiB

Open AccessArticle

Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations

by Joanna Halun, Pawel Karbowniczek, Piotr Kuterba and Zoriana Danel

Entropy 2021, 23(2), 242; https://doi.org/10.3390/e23020242 - 19 Feb 2021

Cited by 3 | Viewed by 2688 | Correction

Abstract

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with

f = 4

arms in a

Θ

-solvent confined in a slit geometry of two parallel walls with repulsive surfaces [...] Read more.

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with

f = 4

arms in a

Θ

-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with

N = 300

, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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10 pages, 370 KiB

Open AccessArticle

Collective Strategy Condensation: When Envy Splits Societies

by Claudius Gros

Entropy 2021, 23(2), 157; https://doi.org/10.3390/e23020157 - 27 Jan 2021

Cited by 3 | Viewed by 2128

Abstract

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. [...] Read more.

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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15 pages, 3941 KiB

Open AccessArticle

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

by Bulcsú Sándor, Bence Schneider, Zsolt I. Lázár and Mária Ercsey-Ravasz

Entropy 2021, 23(1), 103; https://doi.org/10.3390/e23010103 - 12 Jan 2021

Cited by 5 | Viewed by 3766

Abstract

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov [...] Read more.

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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24 pages, 5292 KiB

Open AccessArticle

Butterfly Effect in Chaotic Image Segmentation

by Radu Mărginean, Anca Andreica, Laura Dioşan and Zoltán Bálint

Entropy 2020, 22(9), 1028; https://doi.org/10.3390/e22091028 - 15 Sep 2020

Cited by 6 | Viewed by 2944

Abstract

The exploitation of the important features exhibited by the complex systems found in the surrounding natural and artificial space will improve computational model performance. Therefore, the purpose of the current paper is to use cellular automata as a tool simulating complexity, able to [...] Read more.

The exploitation of the important features exhibited by the complex systems found in the surrounding natural and artificial space will improve computational model performance. Therefore, the purpose of the current paper is to use cellular automata as a tool simulating complexity, able to bring forth an interesting global behaviour based only on simple, local interactions. We show that, in the context of image segmentation, a butterfly effect arises when we perturb the neighbourhood system of a cellular automaton. Specifically, we enhance a classical GrowCut cellular automaton with chaotic features, which are also able to improve its performance (e.g., a Dice coefficient of 71% in case of 2D images). This enhanced GrowCut flavor (referred to as Band-Based GrowCut) uses an extended, stochastic neighbourhood, in which randomly-selected remote neighbours reinforce the standard local ones. We demonstrate the presence of the butterfly effect and an increase in segmentation performance by numerical experiments performed on synthetic and natural images. Thus, our results suggest that, by having small changes in the initial conditions of the performed task, we can induce major changes in the final outcome of the segmentation. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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2 pages, 189 KiB

Open AccessCorrection

Correction: Halun et al. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. Entropy 2021, 23, 242

by Joanna Halun, Pawel Karbowniczek, Piotr Kuterba and Zoriana Danel

Entropy 2022, 24(3), 413; https://doi.org/10.3390/e24030413 - 16 Mar 2022

Viewed by 1614

Abstract

The authors wish to make the following correction to this paper [...] Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

22 pages, 9672 KiB

Open AccessConference Report

Knotting the MECO Network

by Reinhard Folk

Entropy 2021, 23(2), 141; https://doi.org/10.3390/e23020141 - 24 Jan 2021

Cited by 1 | Viewed by 3269

Abstract

The Conferences of the Middle European Cooperation in Statistical Physics (MECO) were created as an attempt to establish and maintain an exchange between scientists in the fields of statistical and condensed matter physics from Western and Eastern countries, overcoming the hurdles of the [...] Read more.

The Conferences of the Middle European Cooperation in Statistical Physics (MECO) were created as an attempt to establish and maintain an exchange between scientists in the fields of statistical and condensed matter physics from Western and Eastern countries, overcoming the hurdles of the Iron Curtain. Based on personal remembrance and historical resources, the genesis and further development of MECO meetings is described. The annual meetings were interrupted in 1991 by the Yugoslav War but were re-established in 1993 and continue today. Although the fall of the Iron Curtain and the European Research programs changed the situation for the meetings considerably, the ties created by MECO still are useful to help scientific exchange. The history of European (and not only) statistical physics and the history of the MECO are tightly intertwined. It started in a time where an essential breakthrough has been achieved in statistical physics describing the features near phase transitions. In addition to the merging of solid-state physics and field theory concepts, the application of numerical methods (Monte Carlo methods) added a new pillar besides exact solutions and experiments to check theoretical models. In the following, the scientific emphasis (in general) has changed from the traditional fields of the first MECO to complexity and interdisciplinary themes as well. Full article

(This article belongs to the Special Issue Selected Papers from 45th Conference of the Middle European Cooperation in Statistical Physics)

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