Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912842875142144 |
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| author | Chun, Hyun-Myung Kwon, Euijoon Park, Hyunggyu Lee, Jae Sung |
| author_facet | Chun, Hyun-Myung Kwon, Euijoon Park, Hyunggyu Lee, Jae Sung |
| contents | We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that generalizes the fluctuation-dissipation theorem from equilibrium to nonequilibrium settings. This relation connects global fluctuations of observables with their local responses to perturbations in force, mobility, and temperature. We further derive finite-time fluctuation-response inequalities, leading to response uncertainty relations that complement the identity by providing more practical bounds. These derivations establish a unified theoretical framework linking the fluctuation-dissipation theorem and thermodynamic uncertainty relations. Using the $F_1$-ATPase molecular motor model, we illustrate how these response-based bounds constrain the long-time diffusion coefficient. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics Chun, Hyun-Myung Kwon, Euijoon Park, Hyunggyu Lee, Jae Sung Statistical Mechanics We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that generalizes the fluctuation-dissipation theorem from equilibrium to nonequilibrium settings. This relation connects global fluctuations of observables with their local responses to perturbations in force, mobility, and temperature. We further derive finite-time fluctuation-response inequalities, leading to response uncertainty relations that complement the identity by providing more practical bounds. These derivations establish a unified theoretical framework linking the fluctuation-dissipation theorem and thermodynamic uncertainty relations. Using the $F_1$-ATPase molecular motor model, we illustrate how these response-based bounds constrain the long-time diffusion coefficient. |
| title | Fluctuation-Response Theory for Nonequilibrium Langevin Dynamics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.16387 |