Thermodynamic Geometry of Relaxation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911598526857216 |
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| author | Wang, Hao Zhao, Li Deng, Shuai Ma, Yu-Han |
| author_facet | Wang, Hao Zhao, Li Deng, Shuai Ma, Yu-Han |
| contents | While the geometry of equilibrium states and driven non-equilibrium processes is clearly understood, a geometric description for relaxation towards equilibrium is still lacking. Here, we propose a thermo-geometric measure based on the Rayleigh quotient, reformulating relaxation as a fundamental competition between entropic stiffness and frictional dissipation. Taking a van der Waals gas with two dissipation channels as an example, we explicitly demonstrate its relaxation landscape. Particularly, we find that upon approaching the critical temperature $T_c$, the slow-mode relaxation rate vanishes linearly as $λ_s \propto (T-T_c)/T_c$, indicating critical slowing down. This study completes the thermodynamic geometry framework, providing a general tool for characterizing the relaxation dynamics of complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamic Geometry of Relaxation Wang, Hao Zhao, Li Deng, Shuai Ma, Yu-Han Statistical Mechanics Classical Physics Quantum Physics While the geometry of equilibrium states and driven non-equilibrium processes is clearly understood, a geometric description for relaxation towards equilibrium is still lacking. Here, we propose a thermo-geometric measure based on the Rayleigh quotient, reformulating relaxation as a fundamental competition between entropic stiffness and frictional dissipation. Taking a van der Waals gas with two dissipation channels as an example, we explicitly demonstrate its relaxation landscape. Particularly, we find that upon approaching the critical temperature $T_c$, the slow-mode relaxation rate vanishes linearly as $λ_s \propto (T-T_c)/T_c$, indicating critical slowing down. This study completes the thermodynamic geometry framework, providing a general tool for characterizing the relaxation dynamics of complex systems. |
| title | Thermodynamic Geometry of Relaxation |
| topic | Statistical Mechanics Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2604.15000 |