A nonequilibrium distribution for stochastic thermodynamics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911551794970624 |
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| author | Garden, Jean-Luc |
| author_facet | Garden, Jean-Luc |
| contents | We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy levels. Within this framework, we derive a microscopic expression for work and introduce a microscopic definition of entropy production (defined here in terms of the uncompensated heat of Clausius) during a nonequilibrium stochastic process. Work and entropy production share a common origin arising from variations of the system energy. The proposed framework allows us to recover the nonequilibrium work relation and to establish a new equivalent identity for the heat exchanged during a work protocol. Finally, we show that the fluctuations of work and heat governed by the extended canonical distribution follow directly from the fluctuation theorem for entropy production. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonequilibrium distribution for stochastic thermodynamics Garden, Jean-Luc Statistical Mechanics We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy levels. Within this framework, we derive a microscopic expression for work and introduce a microscopic definition of entropy production (defined here in terms of the uncompensated heat of Clausius) during a nonequilibrium stochastic process. Work and entropy production share a common origin arising from variations of the system energy. The proposed framework allows us to recover the nonequilibrium work relation and to establish a new equivalent identity for the heat exchanged during a work protocol. Finally, we show that the fluctuations of work and heat governed by the extended canonical distribution follow directly from the fluctuation theorem for entropy production. |
| title | A nonequilibrium distribution for stochastic thermodynamics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.08315 |