Time-resolved statistics of snippets as general framework for model-free entropy estimators

Abstract

Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia, allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time-reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories, for which a generalized detailed balance relation is discussed.

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• Perspective: Time irreversibility in systems observed at coarse resolution
• Effective estimation of entropy production with lacking data
• On the emergence of memory in equilibrium versus non-equilibrium systems
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• Compensating random transition-detection blackouts in Markov networks
• Counting observables in stochastic excursions
• Framework for fluctuating times and counting observables in stochastic excursions
• A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference