Thermodynamic bound on spectral perturbations, with applications to oscillations and relaxation dynamics

Kolchinsky, Artemy; Ohga, Naruo; Ito, Sosuke

doi:http://dx.doi.org/10.1103/physrevresearch.6.013082

Thermodynamic bound on spectral perturbations, with applications to oscillations and relaxation dynamics

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Kolchinsky A, Ohga N, Ito S. Thermodynamic bound on spectral perturbations, with applications to oscillations and relaxation dynamics. Phys Rev Research. 2024 Jan 23;6(1):013082. DOI: 10.1103/physrevresearch.6.013082

Abstract

In discrete-state Markovian systems, many important properties of correlation functions and relaxation dynamics depend on the spectrum of the rate matrix. Here we demonstrate the existence of a universal trade-off between thermodynamic and spectral properties. We show that the entropy production rate, the fundamental thermodynamic cost of a nonequilibrium steady state, bounds the difference between the eigenvalues of a nonequilibrium rate matrix and a reference equilibrium rate matrix. Using this result, we derive thermodynamic bounds on the spectral gap, which governs autocorrelation times and the speed of relaxation to a steady state. We also derive the thermodynamic bounds on the imaginary eigenvalues, which govern the speed of oscillations. We illustrate our approach using a simple model of biomolecular sensing.