Doing statistical mechanics with classical light

I review the concept of thermalization of light in systems of coupled nonlinear optical waveguides within the framework of the tight-binding model with nonlinearity. 

In many cases of interest the energy and power conservation laws enable the formulation of the equilibrium properties of such systems in terms of the Gibbs measure with positive temperature. 

As a particular example I will consider the statistics of two nonlinearly coupled vector fields relevant to the propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. In the limit of the

large nonlinearity an analytical expression for the distribution of Stokes parameters can be obtained which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity.