Effective estimation of entropy production with lacking data

Abstract

Observing stochastic trajectories with rare transitions between states, practically undetectable on time scales accessible to experiments, makes it impossible to directly quantify the entropy production and thus infer whether and how far systems are from equilibrium. To solve this issue for Markovian jump dynamics, we show a lower bound that outperforms any other estimation of entropy production (including Bayesian approaches) in regimes lacking data due to the strong irreversibility of state transitions. Moreover, in the limit of complete irreversibility, our new effective version of the thermodynamic uncertainty relation sets a lower bound to entropy production that depends only on nondissipative aspects of the dynamics. Such an approach is also valuable when dealing with jump dynamics with a deterministic limit, such as irreversible chemical reactions.

V3: published version

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• Dynamical activity universally bounds precision of response in Markovian nonequilibrium systems
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Inferring entropy production from time-dependent moments
• Dissipation at limited resolutions: Power law and detection of hidden dissipative scales
• Force-free kinetic inference of entropy production
• A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production