Nonequilibrium Fluctuation-Response Theory in the Frequency Domain
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913094998949888 |
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| author | Kwon, Euijoon Chun, Hyun-Myung Park, Hyunggyu Lee, Jae Sung |
| author_facet | Kwon, Euijoon Chun, Hyun-Myung Park, Hyunggyu Lee, Jae Sung |
| contents | We develop a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The relation expresses the power spectrum of general observables exactly as a quadratic form of local responses measured at the same frequency, thereby extending static nonequilibrium fluctuation-response relations to finite frequencies. The decomposition is spatial for Langevin systems and edge-resolved for Markov jump processes, and applies uniformly to state-dependent observables, current-like observables, and their combinations. As consequences of the same identity, we derive frequency-domain response uncertainty relations, kinetic and thermodynamic uncertainty relations, the equilibrium fluctuation-dissipation theorem, and Harada-Sasa-type relations. Applications to stochastic networks and driven diffusive systems illustrate how the theory resolves fluctuation spectra into edge-wise contributions and reveals frequency-dependent tradeoffs between fluctuations, response, and dissipation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05038 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonequilibrium Fluctuation-Response Theory in the Frequency Domain Kwon, Euijoon Chun, Hyun-Myung Park, Hyunggyu Lee, Jae Sung Statistical Mechanics We develop a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The relation expresses the power spectrum of general observables exactly as a quadratic form of local responses measured at the same frequency, thereby extending static nonequilibrium fluctuation-response relations to finite frequencies. The decomposition is spatial for Langevin systems and edge-resolved for Markov jump processes, and applies uniformly to state-dependent observables, current-like observables, and their combinations. As consequences of the same identity, we derive frequency-domain response uncertainty relations, kinetic and thermodynamic uncertainty relations, the equilibrium fluctuation-dissipation theorem, and Harada-Sasa-type relations. Applications to stochastic networks and driven diffusive systems illustrate how the theory resolves fluctuation spectra into edge-wise contributions and reveals frequency-dependent tradeoffs between fluctuations, response, and dissipation. |
| title | Nonequilibrium Fluctuation-Response Theory in the Frequency Domain |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2605.05038 |