Measuring Out-of-Equilibrium Fluctuations

In this chapter, we review the measure of the injected and dissipated energy in stochastic systems driven out of equilibrium by external forces. We will focus on systems where the mean injected energy is of the order of thermal fluctuations, which therefore cannot be neglected. We introduce from an experimental point of view the main concepts of fluctuation theorems for work, heat, and entropy production in out-of-equilibrium systems. As an example, we analyze the measurements performed in two experiments: (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 will rapidly describe some consequences of fluctuation theorems and some useful applications to the analysis of experimental data. We discuss the difference between systems driven by a deterministic force and those driven by random forces. Finally, we will use the example of the Brownian particle to analyze the problem of fluctuation-dissipation theorem in out-of-equilibrium systems.