Statistical mechanics of weakly nonlinear optical multimode gases.

By utilizing notions from statistical mechanics, we develop a general and self-consistent theoretical framework capable of describing any weakly nonlinear optical multimode system involving conserved quantities. We derive the fundamental relations that govern the grand canonical ensemble through maximization of the Gibbs entropy at equilibrium. In this classical picture of statistical photo-mechanics, we obtain analytical expressions for the probability distribution, the grand partition function, and the relevant thermodynamic potentials. Our results universally apply to any other weakly nonlinear multimode bosonic system.