Fluctuations and Irreversibility: Historical and Modern Perspectives

TL;DR

The paper traces the historical development of fluctuation theory and its connection to irreversibility, spanning equilibrium to far-from-equilibrium regimes and extending into quantum thermodynamics. It unifies classical fluctuation relations—Evans–Searles, Jarzynski, and Crooks—with linear response theory, culminating in a quantum framework for work fluctuations via the cumulant generating function $K(\lambda)$ and its dissipative part $K^{\rm diss}(\lambda)$. Key contributions include a comprehensive map of fluctuation theorems (including Hatano–Sasa and joint fluctuation theorems), a LRT-based treatment of quantum work fluctuations that predicts positive cumulants and non-Gaussian tails, and a discussion of experimental relevance and TPM limitations. Overall, the work provides a coherent, physics-grounded route to understanding and exploiting irreversibility in quantum thermodynamics for technologies such as quantum computers, sensors, and metrological devices.

Abstract

This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the statistical behaviour of thermodynamic systems far from equilibrium, are now well established. Their quantum counterparts, however, remain an active area of research. In this review, we highlight recent advances by linking quantum fluctuation theorems with linear response theory, offering new insights into the nature of quantum fluctuations and irreversibility in the near-equilibrium regime. Particular emphasis is placed on dissipated work in quantum systems as a pathway to observing non-classical effects in quantum thermodynamics. Understanding quantum fluctuations is not only essential for clarifying the foundations of irreversibility but also crucial for the development of novel quantum technologies, including quantum computers, sensors, and metrological devices.