Universal bounds on entropy production from fluctuating coarse-grained trajectories

Abstract

Entropy production is arguably the most universally applicable measure of non-equilibrium behaviour, particularly for systems coupled to a heat bath. This setting encompasses driven soft matter as well as biomolecular, biochemical and biophysical systems. Despite the central role of entropy production, direct measurements of it remain challenging, especially in small systems dominated by fluctuations. The main difficulty arises because not all degrees of freedom that contribute to entropy production are experimentally accessible. A key question, therefore, is how to infer entropy production from coarse-grained observations, such as time series of experimentally measurable variables. Over the past decade, stochastic thermodynamics has provided several inequalities that yield model-free lower bounds on entropy production from such coarse-grained data. The major approaches rely on observations of coarse-grained states, fluctuating currents or ticks, correlation functions of coarse-grained observables, and waiting-time distributions between ‘Markovian’ events, which correspond to transitions between mesoscopic states. Here, I systematically review these techniques valid under the sole assumption of a Markovian (that is, memoryless) dynamics on an underlying, not necessarily observable, network of states or following a possibly high-dimensional Langevin equation. I discuss in detail the large class of non-equilibrium steady states and highlight extensions of these methods to time-dependent and relaxing systems. Although our focus is on mean entropy production, I also summarize recent progress in quantifying entropy production along individual coarse-grained trajectories. Entropy production quantifies non-equilibrium behaviour but is hard to measure in fluctuating, partially observed systems. This Review discusses stochastic thermodynamics approaches that infer model-free lower bounds from coarse-grained observables, including states, currents, correlations and waiting times, across steady and time-dependent regimes, and highlights progress in trajectory-level estimation.