  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 surprisingly
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.
