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Dissipation-recurrence inequalities at the steady state.

Diego Frezzato1

  • 1Department of Chemical Sciences, University of Padova, Via Marzolo 1, 35131 Padova, Italy.

Physical Review. E
|April 17, 2021
PubMed
Summary

We derived new inequalities for Markov jump processes, linking entropy production to recurrence times. These bounds on entropy production, combined with existing lower bounds, offer insights into the precision of dynamic systems operating out-of-equilibrium.

Area of Science:

  • Non-equilibrium statistical mechanics
  • Theoretical physics
  • Chemical kinetics

Background:

  • Markov jump processes are fundamental models for systems with discrete states and transitions.
  • Understanding entropy production is key to characterizing the irreversibility of dynamic processes.
  • Out-of-equilibrium steady states present unique challenges for thermodynamic analysis.

Purpose of the Study:

  • To establish novel inequalities relating entropy production to recurrence times in Markov jump processes.
  • To derive kinetic inequalities for the precision of dynamical outputs by combining upper and lower bounds.
  • To extend these findings to continuous degrees of freedom, specifically overdamped Markov dynamics.

Main Methods:

  • Derivation of inequalities for discrete-time Markov jump processes.

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  • Extension of methods to continuous systems, focusing on one-dimensional diffusion.
  • Application of finite-time thermodynamic uncertainty relations.

    • Main Results:

    • New upper bounds on the average rate of entropy production are established, linked to site-to-site recurrence timing.
    • Kinetic inequalities for the relative precision of dynamical outputs are derived.
    • An upper bound on average velocity for diffusion in tilted periodic potentials is obtained.

    Conclusions:

    • The derived inequalities provide a deeper understanding of the interplay between entropy production and system dynamics.
    • The results offer a framework for analyzing the efficiency and precision of non-equilibrium systems.
    • The study bridges discrete and continuous descriptions of Markovian dynamics in thermodynamics.