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 non-ideal RJ (NIRJ) -- 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 analogue of the compressibility factor, which controls the transition from an ideal, non-interacting equation of state (EoS) to a van der Waals-like interacting EoS.