An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions

Abstract

A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic bound, we derive an operationally accessible entropy estimator for this observation scenario. We illustrate the operational relevance and the quality of this entropy estimator with a numerical analysis of various representative examples.

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• A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
• Counting observables in stochastic excursions