Estimating Irreversibility in Nonequilibrium Systems using Contrastive Learning

The dynamics of nonequilibrium steady states and out-of-equilibrium processes are intrinsically linked to the arrow of time. This encompasses many complex systems such as the paradigmatic model of coupled oscillators exchanging heat with several baths, and biological processes such as dissipation in the actomyosin cortex powered by ATP hydrolysis. While the arrow of time is well understood in terms of stochastic entropy and transition rates, the practical estimation of the entropy production rate has proven to be challenging for real high-dimensional and nonlinear data. In this work, we propose a new and tractable statistical estimator for measuring reversibility. In contrast with previous methods which estimate the absolute likelihoods of future observations given present conditions, we obtain an estimate of the irreversibility in terms of the relative likelihoods between forward and backward state transitions through a suitable optimization procedure. This is substantially easier to compute and corresponds to the process of learning a classifier which distinguishes between forward (likely) and reverse (unlikely) state transitions. Numerically, we show that this estimator recovers the expected entropy production rates for simple non-equilibrium processes. We also report progress on scaling our method to high-dimensional experimental data in the form of high-resolution videos of biological systems, without requiring coarse-graining or discretization.