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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.06839 |
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| _version_ | 1866912753392812032 |
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| author | Fan, Shuyuan Zhang, Qi |
| author_facet | Fan, Shuyuan Zhang, Qi |
| contents | We analyze the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, a class of stochastic dynamics relevant to nonequilibrium statistical physics. For such nonlocal dynamics, the free energy admits a full dissipation formula that decomposes into entropy production and housekeeping heat. A central result is a decomposition of the generator into symmetric and anti-symmetric parts with respect to the invariant measure $ρ_{ss}$. The symmetric sector corresponds to a reversible dynamics and yields a nonlocal Fisher information governing free-energy decay, whereas the anti-symmetric sector generates a canonical conservative flow that produces circulation but no dissipation. Several numerical examples demonstrate how this decomposition clarifies the structure of nonequilibrium stationary states in jump-driven systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free energy dissipation and a decomposition of general jump diffusions on $\mathbb{R}^n$ without detailed balance Fan, Shuyuan Zhang, Qi Statistical Mechanics Probability 82C31, 82C35 We analyze the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, a class of stochastic dynamics relevant to nonequilibrium statistical physics. For such nonlocal dynamics, the free energy admits a full dissipation formula that decomposes into entropy production and housekeeping heat. A central result is a decomposition of the generator into symmetric and anti-symmetric parts with respect to the invariant measure $ρ_{ss}$. The symmetric sector corresponds to a reversible dynamics and yields a nonlocal Fisher information governing free-energy decay, whereas the anti-symmetric sector generates a canonical conservative flow that produces circulation but no dissipation. Several numerical examples demonstrate how this decomposition clarifies the structure of nonequilibrium stationary states in jump-driven systems. |
| title | Free energy dissipation and a decomposition of general jump diffusions on $\mathbb{R}^n$ without detailed balance |
| topic | Statistical Mechanics Probability 82C31, 82C35 |
| url | https://arxiv.org/abs/2512.06839 |