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Entropy 2008, 10(3), 160-182; doi:10.3390/entropy-e10030010

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

Università di Brescia, via Branze 38, Brescia, I-25123, Italy
Received: 17 December 2007 / Revised: 30 July 2008 / Accepted: 30 July 2008 / Published: 14 August 2008
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Abstract

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.
Keywords: maximum entropy formalism; maximum entropy production; steepest entropy ascent; nonequilibrium dynamics; irreversible thermodynamics; Onsager reciprocity; fluctuation-dissipation relations; entropy generation by irreversibility; nonequilibrium temperature; constrained equilibrium; nonlinear dynamical systems maximum entropy formalism; maximum entropy production; steepest entropy ascent; nonequilibrium dynamics; irreversible thermodynamics; Onsager reciprocity; fluctuation-dissipation relations; entropy generation by irreversibility; nonequilibrium temperature; constrained equilibrium; nonlinear dynamical systems
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Beretta, G.P. 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. Entropy 2008, 10, 160-182.

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