Nonequilibrium Fluctuation-Response Theory in the Frequency Domain

TL;DR

This paper introduces a unified frequency-domain fluctuation-response theory for nonequilibrium steady states, extending classical relations and revealing new insights into fluctuation spectra and response-dissipation tradeoffs.

Contribution

It develops a comprehensive fluctuation-response framework in the frequency domain applicable to Langevin and Markov jump processes, unifying various fluctuation and response relations.

Findings

Derives exact frequency-domain fluctuation-response relations for nonequilibrium systems.

Establishes response uncertainty, kinetic, and thermodynamic uncertainty relations in frequency domain.

Applies the theory to stochastic networks and driven diffusive systems, revealing detailed fluctuation spectra.

Abstract

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.