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Entropy 2013, 15(10), 4345-4375; doi:10.3390/e15104345

Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System

Department of Mechanical Science and Bioengineering, Osaka University, 1-3 Machikaneyama,Toyonaka, Osaka 560-8531, Japan
Received: 5 August 2013 / Revised: 24 September 2013 / Accepted: 9 October 2013 / Published: 16 October 2013
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)
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Abstract

In this study, the balance equation for local entropy density defined on each partition is obtained by the decomposition of the time-evolution operator for local entropy density, on the level of the master equation, by using symmetric and antisymmetric properties for the inversion of partition, density pairs and a given drift velocity. The resultant equation includes the following terms: convection, diffusion, entropy flow due to a thermostat and entropy production. The averaging of the four terms recover the corresponding terms in a balance equation for the macroscopic entropy density of irreversible thermodynamics for a thermostated system. Moreover, an empirical law of order estimation is introduced to explain the limiting behavior of the averaged quantities in the macroscopic limit for the bulk system. The law makes it possible to separate some minor contributions from the major four terms and, for example, to explain the positive entropy production rate in a nonequilibrium state for volume-preserving systems, even if the state is far from steady state. They are numerically confirmed on an invertible, dissipative multibaker chain system, named a circuit model. These properties are independent of partitioning.
Keywords: symmetry-based decomposition; local entropy density; coarse graining; dissipative system; positive entropy production; law of order estimation; multibaker map symmetry-based decomposition; local entropy density; coarse graining; dissipative system; positive entropy production; law of order estimation; multibaker map
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ishida, H. Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System. Entropy 2013, 15, 4345-4375.

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