An introduction to the macroscopic fluctuation theory

The macroscopic fluctuation theory provides a general description, based on the probability of large fluctuation, of non-equilibrium 
stationary states arising from stochastic lattice gases. 
I will review the basis principles of this theory and illustrate in detail the two following general features:
- The presence of long range correlations of the density as a consequence of the non locality of the rate function
- The occurrence of phase transitions in the (large) fluctuations of the total current.