Fluctuations in out-of-equilibrium systems: from theory to experiment

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. We will discuss the important difference between the applications of these concepts to stochastic systems and to a second class of systems (chaotic systems) where the fluctuations are induced either by chaotic flows or by fluctuating driving forces. We will mainly analyze the stochastic systems using the measurements performed in two experiments: (a) a harmonic oscillator driven out of equilibrium by an external force; (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. As an example, the case of a molecular motor will be analyzed in some detail. Finally we will discuss the problems related to the applications of fluctuation theorems to chaotic systems.