Thermodynamic and Kinetic Bounds for Finite-frequency Fluctuation-Response

TL;DR

This paper derives universal bounds on the fluctuation-response relations in nonequilibrium systems at finite frequencies, linking spectral SNR to activity and entropy production, and demonstrates how to infer dissipation from spectral data.

Contribution

It introduces frequency-domain fluctuation-response inequalities for steady-state Markov processes, extending static bounds to finite frequencies and providing practical tools for dissipation inference.

Findings

Spectral SNR bounded by dynamical activity for barrier and entropic perturbations.

Spectral SNR bounded by entropy production rate for state-current observables.

Finite-frequency inequalities enable dissipation inference from power spectra.

Abstract

Fluctuation-response relations encode fundamental constraints on nonequilibrium systems. While time-domain static response is bounded by activity and entropy production, finite-frequency extensions for time-dependent perturbations remain largely unexplored. Here, we derive frequency-domain fluctuation-response inequalities for steady-state Markov processes with time-dependent perturbations. For barrier and entropic perturbations, the spectral signal-to-noise ratio (SNR) is universally bounded by dynamical activity. Furthermore, for state-current observables, the SNR is bounded by the entropy production rate (EPR). We illustrate our results using the F1-ATPase model to infer EPR. These finite-frequency inequalities provide a practical route to infer dissipation from power spectra measurements.