Basis of Local Approach in Classical Statistical Mechanics
Abstract: An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are obtained as well as the simplest solution of these eq...
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| Format: | Article |
| Language: | English |
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MDPI AG
2005-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/7/2/122/ |
| _version_ | 1798040166471827456 |
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| author | Sergey R. Sharov |
| author_facet | Sergey R. Sharov |
| author_sort | Sergey R. Sharov |
| collection | DOAJ |
| description | Abstract: An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are obtained as well as the simplest solution of these equations representing the quasi-local distribution with the temperature pattern being assigned. Unlike the Gibbs's distribution, the energy of interaction with surrounding particles appears in the distribution function, which make possible both evolution in the equilibrium case and fluctuations in the non-equilibrium one. The expression for local entropy is obtained. The derivation of hydrodynamic equations from Boltzmann equation has been analyzed. The hydrodynamic equations obtained from Boltzmann equation were shown to be equations for ideal liquid. Reasons for stochastic description in deterministic Hamilton's systems, conditions of applicability of Poincare's recurrence theorem as well as the problem of irreversibility have been considered. |
| first_indexed | 2024-04-11T22:03:43Z |
| format | Article |
| id | doaj.art-f56f787b492748c494b49b69dfb35e9b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:03:43Z |
| publishDate | 2005-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f56f787b492748c494b49b69dfb35e9b2022-12-22T04:00:48ZengMDPI AGEntropy1099-43002005-04-017212213310.3390/e7020122Basis of Local Approach in Classical Statistical MechanicsSergey R. SharovAbstract: An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are obtained as well as the simplest solution of these equations representing the quasi-local distribution with the temperature pattern being assigned. Unlike the Gibbs's distribution, the energy of interaction with surrounding particles appears in the distribution function, which make possible both evolution in the equilibrium case and fluctuations in the non-equilibrium one. The expression for local entropy is obtained. The derivation of hydrodynamic equations from Boltzmann equation has been analyzed. The hydrodynamic equations obtained from Boltzmann equation were shown to be equations for ideal liquid. Reasons for stochastic description in deterministic Hamilton's systems, conditions of applicability of Poincare's recurrence theorem as well as the problem of irreversibility have been considered.http://www.mdpi.com/1099-4300/7/2/122/ensemble of subsystemsphase volumeevolutional equationsquasi-local distributionsirreversibility |
| spellingShingle | Sergey R. Sharov Basis of Local Approach in Classical Statistical Mechanics Entropy ensemble of subsystems phase volume evolutional equations quasi-local distributions irreversibility |
| title | Basis of Local Approach in Classical Statistical Mechanics |
| title_full | Basis of Local Approach in Classical Statistical Mechanics |
| title_fullStr | Basis of Local Approach in Classical Statistical Mechanics |
| title_full_unstemmed | Basis of Local Approach in Classical Statistical Mechanics |
| title_short | Basis of Local Approach in Classical Statistical Mechanics |
| title_sort | basis of local approach in classical statistical mechanics |
| topic | ensemble of subsystems phase volume evolutional equations quasi-local distributions irreversibility |
| url | http://www.mdpi.com/1099-4300/7/2/122/ |
| work_keys_str_mv | AT sergeyrsharov basisoflocalapproachinclassicalstatisticalmechanics |