Optical Thermodynamics beyond the Weak Nonlinearity Limit

Optical thermodynamics has recently emerged as a theoretical framework describing a Rayleigh-Jeans (RJ) modal power distribution of multimoded nonlinear photonic circuits. However, its applicability is constrained to systems exhibiting weak nonlinear mode-mode interactions. Here, by employing a transfer integral operator, we circumvent this limitation and establish a steady-state interacting RJ modal distribution-referred to as nonideal RJ-with renormalized temperature and optical chemical potential. This also builds a natural bridge with earlier work on grand-canonical statistical-mechanical formulations of discrete nonlinear systems. The theory derives the optical analog of the compressibility factor, which controls the transition from an ideal, noninteracting equation of state (EOS) to a van der Waals-like interacting EOS.