Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium and Back

The fluctuation-dissipation relation is a most remarkable classical result of statistical physics, which allows us to understand nonequilibrium properties of thermodynamic systems from observations of equilibrium phenomena. The modern transient fluctuation relations do the opposite: they allow us to understand equilibrium properties from nonequilibrium experiments. Under proper conditions, the transient relations turn into statements about nonequilibrium steady states, even far from equilibrium. The steady state relations, in turn, generalize the fluctuation-dissipation relations, as they reduce to them when approaching equilibrium. We will review the progress made since Einstein’s work on the Brownian motion, which gradually evolved from the theory of equilibrium macroscopic systems towards an ever deeper understanding of nonequilibrium phenomena, and is now shedding light on the physics of mesoscopic systems. In this evolution, the focus also shifted from small to large fluctuations, which nowadays constitute a unifying factor for different theories. We will conclude illustrating the recently introduced t-mixing property and discussing a fully general and simple response formula, which applies to deterministic dynamics and naturally extends the Green-Kubo theory.