Estimating time-dependent entropy production from non-equilibrium trajectories

• Main Authors: Otsubo, Shun, Manikandan, Sreekanth K, Sagawa, Takahiro, Krishnamurthy, Supriya
• Format: Journal Article
• Language: English
• Published: 04-09-2021
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2010.03852

Communications Physics volume 5, Article number: 11 (2022) The rate of entropy production provides a useful quantitative measure of a
non-equilibrium system and estimating it directly from time-series data from
experiments is highly desirable. Several approaches have been considered for
stationary dynamics, some of which are based on a variational characterization
of the entropy production rate. However, the issue of obtaining it in the case
of non-stationary dynamics remains largely unexplored. Here, we solve this open
problem by demonstrating that the variational approaches can be generalized to
give the exact value of the entropy production rate even for non-stationary
dynamics. On the basis of this result, we develop an efficient algorithm that
estimates the entropy production rate continuously in time by using machine
learning techniques, and validate our numerical estimates using analytically
tractable Langevin models in experimentally relevant parameter regimes. Our
method is of great practical significance since all it requires is time-series
data for the system of interest without requiring prior knowledge of the system
parameters.