Spectral Fluctuation-Dissipation-Response Inequalities

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.