Nonlinear optical thermodynamics from a van der Waals-type mean-field theory

Abstract

Optical thermodynamics offers a distinctive framework for understanding complex phenomena in multimode systems, yet standard ideal-gas-like formulation neglects the effect of nonlinear interaction on thermodynamic quantities, significantly restricting its range of validity. Here, we overcome this limitation by developing a mean-field thermodynamic theory that incorporates the nonlinear renormalization of the mode spectrum. The resulting nonlinear equation of state, analogous to that of the van der Waals for gases, enables the prediction of power-dependent mode localization and the description of optical cooling and heating in photonic Joule-Thomson expansion. Our work establishes a unified thermodynamic perspective on the nonlinear control and transport of optical waves.