Abstract

Co-Authors: Naruo Ohga (the University of Tokyo) and Artemy Kolchinsky (the University of Tokyo) In biological information processing, the cross-correlation between an input a(t) and an output b(t) in a steady state, represented as C τ ab = ⟨a(t)b(t +τ)⟩, is a fundamental measure of information transmission. In an equilibrium state, such cross-correlations exhibit symmetry C τ ab = C τ ba as a consequence of Onsager reciprocity known as microscopic reversibility [1]. Biological information processing is frequently conducted in a non-equilibrium steady state with a thermodynamic driving force Fc such as a chemical potential difference in a cycle c. Such a driving force can be seen in various biological processes, including sensory adaptation, membrane transports, and biological clocks. Several studies in stochastic thermodynamics indicate that non-equilibrium driving could enhance biological information processing. When a driving force is applied, these cross-correlations become asymmetric C τ ab , C τ ba in non-equilibrium steady states, potentially affecting information transmission performance. Here, we have introduced a novel stochastic-thermodynamic bound on the asymmetry of cross¹correlations, serving as an extension of microscopic reversibility for non-equilibrium steady states [2]. This bound was geometrically derived using the isoperimetric inequality in the a-b plane. This bound states that the maximal driving force maxc Fc restricts the degree of asymmetry in the cross-correlations |χab| = limτ→0 |C τ ba − C τ ab|/|2 √ (C τ aa − C 0 aa)(C τ bb − C 0 bb)|. Furthermore, as an application, we also prove the thermodynamic bound on the coherence of noisy oscillations, which was previously conjectured numerically [3]. References [1] H. B. G. Casimir, Rev. Mod. Phys. 17, 343 (1945). [2] N. Ohga, S. Ito, & A. Kolchinsky, to appear in Physical Review Letters (2023). [arXiv:2303.13116] [3] A. C. Barato, & U. Seifert, Phys. Rev. E, 95, 062409 (2017).