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

The entropy production rate is an important quantitative measure of non-equilibrium, and there is a great demand for its estimation solely on the basis of trajectory data from experiments. Meanwhile, thermodynamic uncertainty relations (TURs) are inequalities which give lower bounds on the entropy production rate using only the mean and variance of fluctuating currents. Here, we show that a TUR in the short-time limit can be used to estimate the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics [1]. Specifically, we formulate the short-time TUR both for Markov jump processes and Langevin dynamics, and show that the equality is always achievable in Langevin dynamics, while this is not the case in Markov jump processes. On the basis of the results, we develop an efficient estimation algorithm by combining the short-time TUR with machine learning techniques such as the gradient ascent. We numerically demonstrate that our method performs very well even in nonlinear or high-dimensional Langevin dynamics.

[1] S. Otsubo, S. Ito, A. Dechant, and T. Sagawa, Phys. Rev. E 101, 062106 (2020).