非平衡热力学中的李群：粘塑性背后的几何结构
Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity
摘要：
泊松括号提供了确定非平衡态热力学中动力学现象的可逆贡献所需的数学结构。这种数学结构与李群及其李代数有着深刻的联系。从与一个给定的李代数作为一个通用的覆盖群的代理人的所有李群的特征，我们得到一个自然的分类流变模型的离散参考状态的概念的基础上，特别是，我们发现一个明确的和深刻的区别粘塑性和粘弹性。抽象的想法说明了一个天真的玩具模型的晶体粘塑性，但类似的动力学模型也用于建模的粘塑性行为的眼镜。我们讨论了一些影响粗粒化和统计力学。
英文摘要：
Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
