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Thermodynamic bound on cross-correlations for biological information processing

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SPLW01 - Building a bridge between non-equilibrium statistical physics and biology

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 [2-5]. 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 [6]. 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 [7]. References [1] H. B. G. Casimir, Rev. Mod. Phys. 17, 343 (1945). [2] G. Lan, P. Sartori, S. Neumann, V. Sourjik., & Y. Tu, Nat. Phys. 8, 422 (2012). [3] S. Ito, & T. Sagawa, Nat. Commun. 6, 7498 (2015). [4] A. C. Barato, & U. Seifert, Phys. Rev. X, 6, 041053 (2016). [5] S. Yoshida, Y. Okada, E. Muneyuki, & S. Ito, Phys. Rev. Res. 4, 023229 (2022). [6] N. Ohga, S. Ito, & A. Kolchinsky, arXiv:2303.13116 (2023). [7] A. C. Barato, & U. Seifert, Phys. Rev. E, 95, 062409 (2017).

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