Spectral Fluctuation-Dissipation-Response Inequalities

TL;DR

This paper derives inequalities relating spectral fluctuation, dissipation, and response in Markov processes, providing bounds on FDT violations in nonequilibrium steady states based on measurable quantities.

Contribution

It introduces spectral inequalities that connect fluctuation, dissipation, and response, extending the fluctuation-dissipation theorem to nonequilibrium steady states with experimentally accessible bounds.

Findings

Bounds relate susceptibility mismatch to entropy production and relaxation times.

Standard FDT recovered at equilibrium as a special case.

Provides experimentally testable limits on FDT breakdown.

Abstract

We derive spectral fluctuation--dissipation--response inequalities for finite-state Markov jump processes. By comparing the causal susceptibility to its passive equilibrium reference, we establish frequency-resolved and frequency-integrated inequalities that bound their mismatch in terms of the steady-state entropy production rate, probe variance, short-time perturbation diffusion, and reversible relaxation timescales. Our bounds exactly recover the standard fluctuation--dissipation theorem at equilibrium and apply directly to measurable causal susceptibilities, providing experimentally testable thermodynamic limits on FDT breakdown in driven steady states.