Effective estimation of entropy production with lacking data

TL;DR

This paper introduces a new lower bound for estimating entropy production in Markovian jump processes, especially effective when data is scarce due to rare or irreversible transitions, improving inference of system irreversibility.

Contribution

It presents a novel lower bound for entropy production that outperforms existing methods in data-limited regimes and extends to systems with deterministic limits.

Findings

New lower bound surpasses Bayesian methods in data-limited regimes

Effective thermodynamic uncertainty relation for fully irreversible systems

Applicable to jump dynamics with deterministic limits such as chemical reactions

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.