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  • Letter
  • Open Access

Continuous time reversal and equality in the thermodynamic uncertainty relation

Andreas Dechant and Shin-ichi Sasa

  • Department of Physics 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

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Phys. Rev. Research 3, L042012 – Published 29 October, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042012

Abstract

We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated relative to their local mean value. Moreover, the family of dynamics realizing the continuous time reversal contains an equilibrium dynamics halfway between the time-forward and time-reversed dynamics. We show that this equilibrium dynamics, together with an appropriate choice of the observable, turns the inequality in the TUR into an equality. We demonstrate our findings for the example of a particle diffusing in a tilted periodic potential.

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Phys. Rev. Research 3, L042012– Published 29 October, 2021
  • Received 29 October 2020
  • Revised 10 September 2021
  • Accepted 12 October 2021
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