Spectral Duality and Thermodynamic Bounds on Finite-frequency Fluctuation Responses

Abstract

Fluctuation-response relations encode fundamental constraints on non-equilibrium systems. While time-domain static response is bounded by activity and entropy production, finite-frequency thermodynamic bounds for time-dependent perturbations remain largely unexplored. Here, we find a finite-frequency response-duality relation in non-equilibrium Markov jump processes. For state-current observables, the ratio between the spectral responses to kinetic-barrier and entropic-force perturbations is frequency-independent and gives the single-transition entropy production. The response-duality relation provides a method for measuring the single-transition entropy production from spectral response signals. Furthermore, we derive frequency-domain thermodynamic and kinetic inequalities for non-equilibrium systems with time-dependent perturbations around unperturbed steady states. We illustrate our response-duality relation on a quantum dot system. These finite-frequency response relations and inequalities provide a practical route for inferring dissipation from power-spectrum response measurements.