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Recent experimental developments in multimode nonlinear photonic circuits (MMNPCs), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a nonequilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still terra incognita. Here, by combining Landauer and kinematics formalisms we develop a universal one-parameter scaling theory that describes the whole transport behavior from the ballistic to the diffusive regime, including both positive and negative optical temperature scenarios. We also derive a photonic version of the Wiedemann-Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPCs and may be useful for the design of all-optical cooling protocols.Received 23 October 2023Accepted 4 April 2024DOI:https://doi.org/10.1103/PhysRevLett.132.193802© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical opticsKinetic theoryNonequilibrium & irreversible thermodynamicsNonlinear opticsOptics & lasersTransport phenomenaPhysical SystemsNonequilibrium lattice modelsNonequilibrium systemsOptical fibersWaveguidesTechniquesData analysisFinite-size scalingLinear response theoryMetropolis algorithmMonte Carlo methodsScaling methodsSchroedinger equationAtomic, Molecular & OpticalNonlinear DynamicsStatistical Physics & Thermodynamics
Kurnosov et al. (Wed,) studied this question.