Inferring entropy production from time-dependent moments

Abstract

Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize the performance of the system. Although numerous methods are available to infer the entropy production of stationary systems, there are only a limited number of methods that have been proposed for time-dependent systems and, to the best of our knowledge, none of these methods have been applied to experimental systems. Herein, we develop a general non-invasive methodology to infer a lower bound on the mean total entropy production for arbitrary time-dependent continuous-state Markov systems in terms of the moments of the underlying state variables. The method gives quite accurate estimates for the entropy production, both for theoretical toy models and for experimental bit erasure, even with a very limited amount of experimental data. Directly measuring entropy production from experimental data without prior knowledge of the underlying model is highly desirable, as it quantifies time-irreversibility in non-equilibrium systems and can be used to optimize system performance. In this work, the authors have developed a general methodology to infer entropy production for arbitrary time-dependent systems from its first few moments. The method gives quite accurate estimates both for theoretical examples as well as for experimental data on bit erasure.