Modeling non-equilibrium dynamics of a discrete probability distribution: general rate equation for maximal entropy generation in a maximum-entropy landscape with time-dependent constraints
type: Item
instance of: scholarly article
title: Modeling non-equilibrium dynamics of a discrete probability distribution: general rate equation for maximal entropy generation in a maximum-entropy landscape with time-dependent constraints
zbMATH Open document ID: 1179.82083
published in: Entropy
publication date: 2010-01-29T00:00:00Z
review text: Summary: A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Mathematics Subject Classification ID: 82C03
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 5664132
zbMATH Keywords: maximum entropy formalism
zbMATH Keywords: maximum entropy production
zbMATH Keywords: steepest entropy ascent
zbMATH Keywords: nonequilibrium dynamics
zbMATH Keywords: irreversible thermodynamics
zbMATH Keywords: Onsager reciprocity
zbMATH Keywords: fluctuation-dissipation relations
zbMATH Keywords: entropy generation by irreversibility
zbMATH Keywords: nonequilibrium temperature
zbMATH Keywords: constrained equilibrium
zbMATH Keywords: nonlinear dynamical systems
author: Gian Paolo Beretta
MaRDI profile type: Publication
full work available at URL: entropy-e10030010
OpenAlex ID: W2109851683
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DOI: 10.3390/ENTROPY-E10030010
description: scientific article; zbMATH DE number 5664132