Nonequilibrium Fluctuation-Response Theory in the Frequency Domain

Abstract

We establish a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The central identity is an exact fluctuation-response relation that reconstructs the power spectrum of general observables from local responses measured at the same frequency. This relation applies to state-dependent observables, current-like observables, and their combinations, and reveals how local dynamics shape global fluctuations. From this identity, we derive a hierarchy of relations in the frequency domain, including response uncertainty relations, kinetic and thermodynamic uncertainty relations, the equilibrium fluctuation-dissipation theorem, and Harada-Sasa relations. This establishes an overarching framework for fluctuation-response theory in the frequency domain. Applications to stochastic networks and driven diffusive systems demonstrate how the theory decomposes fluctuation spectra into local contributions and reveals frequency-dependent tradeoffs between fluctuations, response, and dissipation.

16 pages and 3 figures for main text, 14 pages for appendix