4 Maximum Entropy Production and Non-equilibrium Statistical Mechanics

2006 ◽  
pp. 41-55 ◽  
Author(s):  
Roderick C. Dewar
Keyword(s):  
Statistical Mechanics ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Equilibrium Statistical Mechanics ◽  
Maximum Entropy Production ◽  
Non Equilibrium

scholarly journals The maximum entropy production principle: two basic questions

2010 ◽  
Vol 365 (1545) ◽  
pp. 1333-1334 ◽  
Author(s):  
Leonid M. Martyushev
Keyword(s):  
Statistical Mechanics ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Physics ◽  
Overwhelming Majority ◽  
Equilibrium Thermodynamics ◽  
Maximum Entropy Production ◽  
Environmental Systems ◽  
Thermodynamics And Statistical Mechanics ◽  
Non Equilibrium

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to ‘prove’ the principle? We adduce one more proof which is most concise today.

scholarly journals Entropy Production, Entropy Generation, and Fokker-Planck Equations for Cancer Cell Growth

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 147-153
Author(s):  
Salvatore Capotosto ◽  
Bailey Smoot ◽  
Randal Hallford ◽  
Preet Sharma
Keyword(s):  
Statistical Mechanics ◽  
Cancer Cells ◽  
Entropy Production ◽  
Cancer Cell ◽  
Entropy Generation ◽  
Normal Growth ◽  
Equilibrium Statistical Mechanics ◽  
Fokker Planck Equations ◽  
Non Equilibrium ◽  
Fokker Planck

It is rather difficult to understand biological systems from a physics point of view, and understanding systems such as cancer is even more challenging. There are many factors affecting the dynamics of a cancer cell, and they can be understood approximately. We can apply the principles of non-equilibrium statistical mechanics and thermodynamics to have a greater understanding of such systems. Very much like other systems, living systems also transform energy and matter during metabolism, and according to the First Law of Thermodynamics, this could be described as a capacity to transform energy in a controlled way. The properties of cancer cells are different from regular cells. Cancer is a name used for a set of malignant cells that lost control over normal growth. Cancer can be described as an open, complex, dynamic, and self-organizing system. Cancer is considered as a non-linear dynamic system, which can be explained to a good degree using techniques from non-equilibrium statistical mechanics and thermodynamics. We will also look at such a system through its entropy due to to the interaction with the environment and within the system itself. Here, we have studied the entropy generation versus the entropy production approach, and have calculated the entropy of growth of cancer cells using Fokker-Planck equations.

scholarly journals An Introduction to the Non-Equilibrium Steady States of Maximum Entropy Spike Trains

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 884 ◽  
Author(s):  
Rodrigo Cofré ◽  
Leonardo Videla ◽  
Fernando Rosas
Keyword(s):  
Statistical Mechanics ◽  
Maximum Entropy ◽  
Spike Trains ◽  
Biological Processes ◽  
Comprehensive Overview ◽  
Equilibrium Statistical Mechanics ◽  
Temporal Asymmetry ◽  
Key Concepts ◽  
Mathematical Foundations ◽  
Non Equilibrium

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical mechanics. This tutorial provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics.

scholarly journals An Introduction to the Non-Equilibrium Steady States of Maximum Entropy Spike Trains

2019 ◽  
Author(s):  
Rodrigo Cofre ◽  
Leonardo Videla ◽  
Fernando Rosas
Keyword(s):  
Statistical Mechanics ◽  
Maximum Entropy ◽  
Spike Trains ◽  
Biological Processes ◽  
Comprehensive Overview ◽  
Equilibrium Statistical Mechanics ◽  
Temporal Asymmetry ◽  
Key Concepts ◽  
Time Irreversibility ◽  
Non Equilibrium

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the3literature of non-equilibrium statistical mechanics. This article provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the5mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics

scholarly journals Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy

2015 ◽  
Vol 22 (2) ◽  
pp. 187-196 ◽  
Author(s):  
M. Mihelich ◽  
D. Faranda ◽  
B. Dubrulle ◽  
D. Paillard
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Passive Scalar ◽  
Scalar Transport ◽  
Zero Range Process ◽  
Maximum Entropy Production ◽  
Passive Scalar Transport ◽  
Optimal Resolution ◽  
Principle Of Maximum ◽  
Non Equilibrium

Abstract. We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy, seen as functions of a parameter f connected to the jump probability, admit a unique maximum denoted fmaxEP and fmaxKS. The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this paper is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation from equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of those adopted by Paltridge and climatologists working on maximum entropy production (N ≈ 10–100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second-order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non-equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

scholarly journals Entropy production at weak Gibbs measures and a generalized variational principle

2009 ◽  
Vol 29 (4) ◽  
pp. 1327-1347 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Variational Principle ◽  
Statistical Mechanics ◽  
Entropy Production ◽  
Invariant Measures ◽  
Stationary Process ◽  
Gibbs Measures ◽  
Generalized Variational Principle ◽  
Probability Measures ◽  
Equilibrium Statistical Mechanics ◽  
Non Equilibrium

AbstractWe consider piecewise invertible systems exhibiting intermittency and establish a generalized variational principle adapted to a non-stationary process in the following sense; the supremum is attained by non-singular (not necessarily invariant) probability measures and if the system exhibits hyperbolicity, then it reduces to the usual variational principle for the pressure. Our method relies on Ruelle’s program in the study of non-equilibrium statistical mechanics to analyze dissipative phenomena. We show non-positivity of entropy production at weak Gibbs measures and clarify when it indeed vanishes. We also discuss a generalized variational principle in the context of σ-finite invariant measures.

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