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 tosystems 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 asnon-ideal RJ (NIRJ)— with renormalized temperature and optical chemical potential. This also builds a naturalbridge 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.