A brief introduction to the inference of entropy production through the fluctuations of currents

Institute for Complex Systems CNR - P.le Aldo Moro 2, 00185, Rome, Italy, Department of Physics, University of Rome “La Sapienza” - P.le Aldo Moro 5, 00185 Rome, Italy and INFN, Sezione Roma2 - Via della Ricerca Scientifica 1, 00133, Rome, Italy

Received: 5 March 2025
Accepted: 2 June 2025

Abstract

Entropy production (EP) serves as a key indicator of a system's departure from thermodynamic equilibrium. However, its general definition, reliant on the probability of paths in the system's phase space, is often abstract. Even with a known system model, EP's physical accessibility remains uncertain. Without a model, the general definition is limited to simple systems with few observables, necessitating estimation methods. This Perspective briefly surveys recent literature on EP estimates derived from theoretical bounds based on observable current fluctuations, particularly Thermodynamic Uncertainty Relations (TURs). We discuss several recent applications. In particular we focus on two problems: 1) a recent conjecture relating the deviations from the TUR bound to internal correlations in the system, considered also in experiments with flagellar beating; 2) the application of the TUR to predict the mean squared diffusion in complex multiple scale dynamics, which also yields a criterion to discriminate equilibrium from non-equilibrium in certain cases.