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.

中文翻译：

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非线性多模光子网络的光动力学理论

最近多模非线性光子电路（MMNPC）的实验发展推动了描述初始光束激发的平衡特性的光学热力学理论的发展。然而，当这些系统与热储层接触时，它们的非平衡输运理论仍然是未知领域。在这里，通过结合兰道尔和运动学形式主义，我们开发了一种通用的单参数标度理论，该理论描述了从弹道到扩散状态的整个输运行为，包括正和负光学温度场景。我们还推导出了连接热导率和功率导率的维德曼-弗朗茨定律的光子版本。我们的工作为从根本上理解 MMNPC 的传输特性铺平了道路，并且可能对全光学冷却协议的设计有用。