Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility

Abstract

Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom, some form of effective, coarse-grained dynamics naturally emerges for which the principles of stochastic thermodynamics generally cease to be applicable straightforwardly. Our work unifies the notion of entropy production along an individual trajectory with that of a coarse-grained dynamics by establishing a framework based on snippets and Markovian events as fundamental building blocks. A key asset of a trajectory-based fluctuating entropy production is the ability to localize individual contributions to the total entropy production in time and space. As an illustration and potential application for inference we introduce a method for the detection of hidden driving. The framework applies equally to even and odd variables and, therefore, includes the peculiar case of entropy production in underdamped Langevin dynamics.

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• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Inferring kinetics and entropy production from observable transitions in partially accessible, periodically driven Markov networks
• Entropy production from waiting-time distributions for overdamped Langevin dynamics
• From observed transitions to hidden paths in Markov networks
• Characteristic oscillations in frequency-resolved heat dissipation of linear time-delayed Langevin systems: Approach from the violation of the fluctuation-response relation
• Counting observables in stochastic excursions
• A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
• Macroscopicity and observational deficit in states, operations, and correlations