The convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention. The sheer complexity associated with such multimode systems, allows them to display a host of phenomena that are otherwise impossible in few-mode settings. At the same time, however, it introduces a set of fundamental challenges in terms of comprehending and harnessing their response. Here, we develop an optical thermodynamic approach capable of describing the thermalization dynamics in large scale nonlinear photonic tight-binding networks. For this specific system, an optical Sackur-Tetrode equation is obtained that explicitly provides the optical temperature and chemical potential of the photon gas. Processes like isentropic expansion/compression, Joule expansion, as well as aspects associated with beam cleaning/cooling and thermal conduction effects in such chain networks are discussed. Our results can be used to describe in an effortless manner the exceedingly complex dynamics of highly multimoded nonlinear bosonic systems.

严重的多模光子结构的复杂的非线性行为是近来引起人们广泛关注的焦点。与这种多模式系统相关的绝对复杂性，使它们能够显示许多现象，而在少数模式设置中是不可能的。但是，与此同时，它在理解和利用响应方面提出了一系列基本挑战。在这里，我们开发了一种光学热力学方法，能够描述大规模非线性光子紧束缚网络中的热动力学。对于此特定系统，获得了光学Sackur-Tetrode方程，该方程明确提供了光子气体的光学温度和化学势。等熵膨胀/压缩，焦耳膨胀，以及与这种链状网络中的束清洁/冷却和热传导效应相关的方面都进行了讨论。我们的结果可以轻松地描述高度多模态非线性玻色子系统的极其复杂的动力学。