Estimating entropy production with odd-parity state variables via machine learning

Abstract

Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path probability distribution, many methods have been developed to estimate EP from only trajectory data. However, for systems with odd-parity variables that prevail in nonequilibrium systems, EP estimation via machine learning has not been covered. In this study, we develop a machine-learning method for estimating the EP in a stochastic system with odd-parity variables through multiple neural networks, which enables us to measure EP with only trajectory data and parity information. We demonstrate our method with two systems, an underdamped bead-spring model and a one-particle odd-parity Markov jump process.