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

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  • Artemy Kolchinsky
    ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Spain
  • Naruo Ohga
    Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • Sosuke Ito
    Universal Biology Institute, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Description

<jats:p>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.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>

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