论文标题
NOETHE不变性波动的差异
Variance of fluctuations from Noether invariance
论文作者
论文摘要
通过其方差衡量的波动强度在大量物理系统的定量描述中至关重要，从简单和复杂的液体到活性流体和固体。波动源于热自由度和统计力学的不规则运动有助于其描述。在这里，我们证明波动受到给定系统的固有对称性的约束。对于基于粒子的经典多体系统，在对称参数中以二阶为二阶的Noether不变性导致确切的总和规则。这些身份与平均势能曲率相互关联。这些不同的机制之间的确切平衡恢复了Noeth的不变性。总和规则提供了评估和构建理论，确保模拟工作中的自符合性以及为波动理论量化提供系统的途径的实用指南。
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from the irregular motion of thermal degrees of freedom and statistical mechanics facilitates their description. Here we demonstrate that fluctuations are constrained by the inherent symmetries of the given system. For particle-based classical many-body systems, Noether invariance at second order in the symmetry parameter leads to exact sum rules. These identities interrelate the global force variance with the mean potential energy curvature. Noether invariance is restored by an exact balance between these distinct mechanisms. The sum rules provide a practical guide for assessing and constructing theories, for ensuring self-consistency in simulation work, and for providing a systematic pathway to the theoretical quantification of fluctuations.
