Matrix approach to generalized ensemble theory for nonequilibrium discrete systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915655002882048 |
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| author | Guan, Shaohua |
| author_facet | Guan, Shaohua |
| contents | A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix approach to generalized ensemble theory for nonequilibrium discrete systems Guan, Shaohua Statistical Mechanics A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems. |
| title | Matrix approach to generalized ensemble theory for nonequilibrium discrete systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2503.17898 |