We discuss the role of thermodynamics in non-linear stability analysis of spatially distributed dissipative systems governed by non-linear partial differential equations. We document profound interplay between various concepts in thermodynamics on one side and non-linear stability analysis on the other side, and subsequently we summarize and comment on various results regarding the non-linear stability of thermodynamically isolated as well as thermodynamically open systems.

中文翻译：

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非线性稳定性和非平衡热力学——来来回回

我们讨论了热力学在由非线性偏微分方程控制的空间分布耗散系统的非线性稳定性分析中的作用。我们一方面记录了热力学中的各种概念与另一方面的非线性稳定性分析之间的深刻相互作用，随后我们总结和评论了关于热力学孤立系统和热力学开放系统的非线性稳定性的各种结果。