Fluctuations, Linear Response, and Currents in Out-of-Equilibrium Systems

In this review we discuss, from an experimental point of view, several concepts of statistical mechanics for systems that are out of equilibrium either because they are driven by external forces or because they are slowly relaxing toward equilibrium. We focus on the case where the mean injected energy is of the order of thermal fluctuations, which therefore cannot be neglected. We first introduce the main concepts of fluctuation theorems (FTs) for work and heat using measurements of (a) a harmonic oscillator driven out of equilibrium by an external force and (b) a colloidal particle trapped in a time-dependent double-well potential. We use the example of the Brownian particle to analyze the problem of the fluctuation-dissipation relation (FDR) in out-of-equilibrium systems. We next study the fluctuations of the position of a Brownian particle inside an aging gelatin after a fast quench. Using the experimental data of this experiment, we show that the mean heat flux is quantitatively related to the violation of the equilibrium fluctuation-dissipation theorem or equivalently to the entropy production rate. Finally, we discuss briefly the problems and the new directions for the stochastic thermodynamics.