Learning entropy production via neural networks

Abstract

This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories without any prior knowledge of the system. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead-spring and discrete flashing ratchet models, and also demonstrate that our method is applicable to high-dimensional data and non-Markovian systems.Nonequilibrium states are ubiquitously observed from colloidal particles to biological systems [1][2][3][4][5][6]. Injection of energy, lack of relaxation time, or broken detailed balance are ordinary sources of nonequilibrium, and in general, such systems are in contact with a heat bath such as a fluid. Thus, to describe the behavior of a nonequilibrium system, it is necessary to investigate the energetics of the system; however, experimentally, heat flow is difficult to measure directly [7][8][9][10]. In this case, measuring the entropy production (EP) can be one remedy to estimate heat flow in a nonequilibrium system [10][11][12].

Estimating entropy production by machine learning of short-time fluctuating currents

“…Since the demand for estimation of the entropy production is ubiquitous [50][51][52][53], various estimators of the entropy production have been investigated. While some of them are based on the fluctuation theorem [54][55][56][57][58], the TUR provides a simpler strategy for estimating the entropy production rate. For the latter, in fact, we only need to know the mean and the variance of a current by adopting the following procedure: Find a current that maximizes the right-hand side (rhs) of Eq.…”