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.光学热力学（Optical thermodynamics）近年来作为一种理论框架被提出，用于描述多模非线性光子电路的瑞利-金斯（Rayleigh-Jeans, RJ）模态功率分布。然而其适用范围仅局限于存在弱非线性模态间相互作用的系统。本文借助转移积分算子（Transfer Integral Operator）突破了这一局限，构建了稳态相互作用型RJ模态分布——即非理想RJ（NIRJ）分布，并引入了重整化温度与光学化学势。该研究同时为此前针对离散非线性系统的巨正则统计力学表述相关工作搭建了天然桥梁。本理论推导了压缩因子的光学类比形式，该因子调控着从理想无相互作用状态方程（EoS）到范德瓦尔斯型相互作用状态方程的过渡。