Macroscopic fluctuations in non-equilibrium systems

Many natural systems are maintained in a stationary state through continuous exchange of matter, energy or information with their surroundings. These various currents break time-reversal
by generating a continuous increase of entropy.  The behaviour of such non-equilibrium systems can not be accounted for by the Principles of  Thermodynamics or by the Gibbs-Boltzmann laws of statistical physics. Although linear response theory and the Onsager-Machlup functional provide useful descriptions of large scale fluctuations in driven systems, they are only valid, at first order, in the vicinity of equilibrium.

In the last two decades, important advances in our understanding of processes far from equilibrium
have been achieved, for which rare events, large deviations and fluctuations relations provide a
unified framework. The emergence of universal features can be studied thanks to a variational
principle, proposed by G. Jona-Lasinio and his collaborators, known as the Macroscopic Fluctu-
ation Theory (MFT). In this theory, optimal fluctuations far from equilibrium are determined at
a coarse-grained scale by two coupled non-linear hydrodynamic equations. The objective of this
talk is to present these concepts and to illustrate them with some exact solutions of the MFT
equations.