Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System
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, dens...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2013-10-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/15/10/4345 |
| _version_ | 1828113925712904192 |
|---|---|
| author | Hideshi Ishida |
| author_facet | Hideshi Ishida |
| author_sort | Hideshi Ishida |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:16:39Z |
| format | Article |
| id | doaj.art-db2f5bf29836409098e8c8655b8eca2a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:16:39Z |
| publishDate | 2013-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-db2f5bf29836409098e8c8655b8eca2a2022-12-22T04:24:18ZengMDPI AGEntropy1099-43002013-10-0115104345437510.3390/e15104345Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain SystemHideshi IshidaIn 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.http://www.mdpi.com/1099-4300/15/10/4345symmetry-based decompositionlocal entropy densitycoarse grainingdissipative systempositive entropy productionlaw of order estimationmultibaker map |
| spellingShingle | Hideshi Ishida Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System Entropy symmetry-based decomposition local entropy density coarse graining dissipative system positive entropy production law of order estimation multibaker map |
| title | Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System |
| title_full | Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System |
| title_fullStr | Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System |
| title_full_unstemmed | Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System |
| title_short | Symmetry-Based Balance Equation for Local Entropy Density in a Dissipative Multibaker Chain System |
| title_sort | symmetry based balance equation for local entropy density in a dissipative multibaker chain system |
| topic | symmetry-based decomposition local entropy density coarse graining dissipative system positive entropy production law of order estimation multibaker map |
| url | http://www.mdpi.com/1099-4300/15/10/4345 |
| work_keys_str_mv | AT hideshiishida symmetrybasedbalanceequationforlocalentropydensityinadissipativemultibakerchainsystem |