Measurement of irreversibility and entropy production via the tubular ensemble

Abstract

The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiment since the probability of a single trajectory is zero. We regularize this definition by considering, instead, the limiting ratio of probabilities for trajectories to remain in the tubular neighborhood of a smooth path and its time reversal. The resulting pathwise medium entropy production agrees with the formal expression from stochastic thermodynamics, and can be obtained from measurable tube probabilities. Estimating the latter from numerically sampled trajectories for Langevin dynamics yields excellent agreement with theory. By combining our measurement of pathwise entropy production with a Markov Chain Monte Carlo algorithm, we infer the entropy-production distribution for a transition path ensemble directly from short recorded trajectories. Our work enables the measurement of irreversibility along individual paths, and path ensembles, in a model-free manner.

12 pages, 5 figures

References in corpus (8)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Inferring entropy production from short experiments
• Estimating entropy production by machine learning of short-time fluctuating currents
• Measurement of Stochastic Entropy Production
• Functionals in stochastic thermodynamics: how to interpret stochastic integrals
• Experimental measurement of relative path probabilities and stochastic actions
• Stochastic action for tubes: Connecting path probabilities to measurement

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• Inferring nonequilibrium thermodynamics from tilted equilibrium using information-geometric Legendre transform
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference