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Measuring entropy production of a system directly from the experimental datais highly desirable since it gives a quantifiable measure of thetime-irreversibility for non-equilibrium systems and can be used as a costfunction to optimize the performance of the system. Although numerous methodsare available to infer the entropy production of stationary systems, there areonly a limited number of methods that have been proposed for time-dependentsystems and, to the best of our knowledge, none of these methods have beenapplied to experimental systems. Herein, we develop a general non-invasivemethodology to infer a lower bound on the mean total entropy production forarbitrary time-dependent continuous-state Markov systems in terms of themoments of the underlying state variables. The method gives surprisinglyaccurate estimates for the entropy production, both for theoretical toy modelsand for experimental bit erasure, even with a very limited amount ofexperimental data.

Inferring entropy production from time-dependent moments