Optical thermodynamics is a recently developed theory that utilizes principles of statistical mechanics in weakly nonlinear multimoded optical settings. Using optical thermodynamics the collective behavior of utterly complex system such as multimode and multicore fibers, waveguide arrays, and coupled microresonators among others, can be unveiled in a physically meaningful context. We analyze fundamental properties that lie in he core of this theory. Specifically, we find that the extensive parameters of the entropy are naturally provided by the propagation constants. Thus, they can be different depending on the system under investigation. We investigate a variety of continuous and discrete settings. In the case of polyatomic lattices, different optomechanical pressures can be defined for each bond. In addition, we develop a theory that can be used to define pressure in systems with non-abrupt boundaries, such as graded index multimode fibers. We analyze the limitations of the Rayleigh-Jeans distribution which might lead to decreasing entropy and pressure singularities.