Thermodynamic Bound on the Asymmetry of Cross-Correlations

Abstract

The principle of microscopic reversibility says that, in equilibrium, two-time cross-correlations are symmetric under the exchange of observables. Thus, the asymmetry of cross-correlations is a fundamental, measurable, and often-used statistical signature of deviation from equilibrium. Here we find a simple and universal inequality that bounds the magnitude of asymmetry by the cycle affinity, i.e., the strength of thermodynamic driving. Our result applies to a large class of systems and all state observables, and it suggests a fundamental thermodynamic cost for various nonequilibrium functions quantified by the asymmetry. It also provides a powerful tool to infer affinity from measured cross-correlations, in a different and complementary way to the thermodynamic uncertainty relations. As an application, we prove a thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured by Barato and Seifert [Phys. Rev. E 95, 062409 (2017)]. We also derive a thermodynamic bound on directed information flow in a biochemical signal transduction model.Received 11 April 2023Accepted 8 June 2023DOI:https://doi.org/10.1103/PhysRevLett.131.077101Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsStochastic thermodynamicsPhysical SystemsBiological networksNonequilibrium systemsTechniquesGeometryMarkovian processesMaster equationBiological PhysicsStatistical PhysicsInterdisciplinary PhysicsNonlinear Dynamics