  Statistical mechanics can provide a versatile theoretical framework for
investigating the collective dynamics of weakly nonlinear waves-settings that
can be utterly complex to describe otherwise. In optics, composite systems
arise due to interactions between different frequencies and/or polarizations.
The purpose of this work is to develop a thermodynamic theory that takes into
account the synergistic action of multiple components. We find that the type of
the nonlinearity involved can have important implications in the thermalization
process and, hence, can lead to different thermal equilibrium conditions.
Importantly, we derive closed-form expressions for the actual optomechanical
pressure that is exerted on the system. In particular, the total optomechanical
pressure is the sum of the partial pressures due to each component. Our results
can be applied to a variety of weakly nonlinear optical settings such as
multimode fibers, bulk waveguides, photonic lattices, and coupled
microresonators. We present two specific examples, where two colors interact in
a waveguide array with either a cubic or quadratic nonlinearity.
