Dissipative timescales from coarse-graining irreversibility

A goal of stochastic thermodynamics research is the development of methods to identify the degrees of freedom responsible for energy dissipation in nonequilibrium steady-states. To complement these efforts, we present a method for estimating the time-scale of dissipative processes modeled as steady-state Markov jump processes on discrete-state spaces. The method exploits an inequality between the entropy production and the irreversibility–the statistical breaking of time-reversal symmetry. We show that when there is a time-scale separation between the dissipative and non-dissipative processes, the irreversibility as a function of the coarse-graining time gives rise to a sigmoid-like profile with a drop off at a coarse-graining time that is inversely proportional to the rate of dissipation. From these observations we derive a functional form that estimates the irreversibility in this highly dissipative regime. Using this functional form as a fitting ansatz, we then propose a method to measure this dissipative time-scale from time-series data, and benchmark it using synthetic data. This method thus lends itself to experimental applications where the rate of dissipative processes are of interest and unknown.