Nonlinear Response Identities and Bounds for Nonequilibrium Steady States
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910038334898176 |
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| author | Bao, Ruicheng Liang, Shiling |
| author_facet | Bao, Ruicheng Liang, Shiling |
| contents | Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of nonequilibrium systems, a theory for the nonlinear regime under finite perturbations has been lacking. Here, building on a novel connection between response and mean first-passage times in continuous-time Markov chains, we derive a comprehensive theory for the nonlinear response to archetypal local perturbations. We establish an exact identity that universally connects the nonlinear response of any observable to its linear counterpart via a simple scaling factor. This identity directly yields universal bounds on the response magnitude. Furthermore, we establish a universal bound on response resolution -- an inequality constraining an observable's change by its intrinsic fluctuations -- thereby setting a fundamental limit on signal-to-noise ratio. These results provide a rigorous and general framework for analyzing nonlinear response far from equilibrium, which we illustrate with an application to transcriptional regulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Response Identities and Bounds for Nonequilibrium Steady States Bao, Ruicheng Liang, Shiling Statistical Mechanics Biological Physics Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of nonequilibrium systems, a theory for the nonlinear regime under finite perturbations has been lacking. Here, building on a novel connection between response and mean first-passage times in continuous-time Markov chains, we derive a comprehensive theory for the nonlinear response to archetypal local perturbations. We establish an exact identity that universally connects the nonlinear response of any observable to its linear counterpart via a simple scaling factor. This identity directly yields universal bounds on the response magnitude. Furthermore, we establish a universal bound on response resolution -- an inequality constraining an observable's change by its intrinsic fluctuations -- thereby setting a fundamental limit on signal-to-noise ratio. These results provide a rigorous and general framework for analyzing nonlinear response far from equilibrium, which we illustrate with an application to transcriptional regulation. |
| title | Nonlinear Response Identities and Bounds for Nonequilibrium Steady States |
| topic | Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2412.19602 |