Thermodynamic correlation inequalities for finite times and transients
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| Format: | Preprint |
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2025
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| _version_ | 1866915286964240384 |
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| author | Dieball, Cai Godec, Aljaž |
| author_facet | Dieball, Cai Godec, Aljaž |
| contents | Recently, a thermodynamic bound on correlation times was formulated in [A. Dechant, J. Garnier-Brun, S.-i. Sasa, Phys. Rev. Lett. 131, 167101 (2023)], showing how the decay of correlations in Langevin dynamics is bounded by short-time fluctuations and dissipation. Whereas these original results only address very long observation times in steady-state dynamics, we here generalize the respective inequalities to finite observations and general initial conditions. We utilize the connection between correlations and the fluctuations of time-integrated density functionals and generalize the direct stochastic calculus approach from [C. Dieball and A. Godec, Phys. Rev. Lett. 130, 087101 (2023)] which paves the way for further generalizations. We address the connection between short and long time scales, as well as the saturation of the bounds via complementary spectral-theoretic arguments. Motivated by the spectral insight, we formulate all results also for complex-valued observables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamic correlation inequalities for finite times and transients Dieball, Cai Godec, Aljaž Statistical Mechanics Mathematical Physics Probability Recently, a thermodynamic bound on correlation times was formulated in [A. Dechant, J. Garnier-Brun, S.-i. Sasa, Phys. Rev. Lett. 131, 167101 (2023)], showing how the decay of correlations in Langevin dynamics is bounded by short-time fluctuations and dissipation. Whereas these original results only address very long observation times in steady-state dynamics, we here generalize the respective inequalities to finite observations and general initial conditions. We utilize the connection between correlations and the fluctuations of time-integrated density functionals and generalize the direct stochastic calculus approach from [C. Dieball and A. Godec, Phys. Rev. Lett. 130, 087101 (2023)] which paves the way for further generalizations. We address the connection between short and long time scales, as well as the saturation of the bounds via complementary spectral-theoretic arguments. Motivated by the spectral insight, we formulate all results also for complex-valued observables. |
| title | Thermodynamic correlation inequalities for finite times and transients |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2503.10599 |