Many natural systems can be maintained in a stationary state through the exchange of matter, energy or information with their surroundings. These various currents break time-reversal invariance, generating a continuous increase of entropy in the universe. Such systems are out of equilibrium and can not be described by the Laws of Thermodynamics, or by using the classical Gibbs-Boltzmann principles of statistical physics.
 
In the last two decades, important advances in our understanding of non-equilibrium processes have been achieved, for which rare events, large deviations and uctuations 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 Fluctuation 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.