Identification and quantification of irreversibility in stochastic systems

Advances in single-molecule measurements, active-matter control, and nonequilibrium statistical mechanics are transforming our understanding of thermodynamics in small, strongly fluctuating systems. Biological molecular motors, driven chemical-reaction networks (e.g., gene regulation), artificial active matter, autonomous engines, and synthetic nanomachines all operate via inherently irreversible, dissipative processes in noisy environments, while producing entropy. Quantifying this entropy production (EP) has therefore become central to understanding both the physical limits and design principles of nanoscale systems. This review surveys principled routes to characterize and quantify EP from time-series and trajectory data. Because experimental observables are often coarse-grained and only partially resolve the underlying dynamics, we discuss how dissipation can be inferred from incomplete information, and how coarse-graining systematically biases EP estimates. This overview maps the current toolkit for estimating EP and outlines open challenges in unifying inference approaches to obtain reliable and tight bounds on EP in living and engineered nanoscale systems.