Probability inequalities for direct and inverse dynamical outputs in driven fluctuating systems

Diego Frezzato
Phys. Rev. E 107, 014112 – Published 13 January 2023

Abstract

When a fluctuating system is subjected to a time-dependent drive or nonconservative forces, the direct-inverse symmetry of the dynamics can be broken so inducing an average bias. Here we start from the fluctuation theorem, a cornerstone of stochastic thermodynamics, for inspecting the unbalancing between direct and inverse dynamical outputs, here called “events,” in a bidirectional forward-backward setup. The occurrence of an event might correspond to the realization of a quantitative output, or to the realization of a sequence of acts that compose a complex “narrative.” The focus is on mutual bounds between the probabilities of occurrence of direct and inverse events in the forward and backward mode. The inspection is made for systems in contact with a thermal bath, and by assuming Markov dynamics on the uncontrolled degrees of freedom. The approach comprises both the case of systems under a time-dependent drive and time-independent external forces. The general formulation is then used to derive (or re-derive) specialized results valid for finite-time processes, and for systems taken into steady conditions (either periodic steady states or steady states) starting from equilibrium. Among the results, we find already known forms of “generalized” thermodynamic uncertainty relations, and derive useful constraints concerning the work distribution function for systems in steady conditions.

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  • Received 17 June 2022
  • Revised 20 October 2022
  • Accepted 21 December 2022

DOI:https://doi.org/10.1103/PhysRevE.107.014112

©2023 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Diego Frezzato*

  • Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131 Padova, Italy

  • *diego.frezzato@unipd.it

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Vol. 107, Iss. 1 — January 2023

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