Continuous time-reversal and equality in the thermodynamic uncertainty relation

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.

18 pages, 2 figures

References in corpus (9)

• Thermodynamic uncertainty relation for biomolecular processes
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Thermodynamic uncertainty relation for time-dependent driving
• Inferring entropy production from short experiments
• Estimating entropy production by machine learning of short-time fluctuating currents
• Entropy production estimation with optimal current
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Effect of a magnetic field on the thermodynamic uncertainty relation

Cited by in corpus (3)

• Optimal thermodynamic uncertainty relation in Markov jump processes
• Universal form of thermodynamic uncertainty relation for Langevin dynamics
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving