Variance of fluctuations from Noether invariance

Hermann, Sophie; Schmidt, Matthias

doi:10.48550/arxiv.2203.15654

Cited by 1 publication

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The section on 'methods' in reference [14] gives a detailed description of the relationship of the equilibrium Noether sum rules to such classical results from the liquid state literature. Together with the nonequilibrium Ornstein-Zernike relations [42,43] the dynamical sum rules provide fertile ground for making progress in nonequilibrium many-body physics; see also the recent study of the relevance of invariance in inhomogeneous dense liquids [72] and of the role of fluctuations when going to effects that are higher than linear in the displacement [73]. Hence the fundamental character of Emmy Noether's work will surely continue to prove its worth in the future.…”

Section: Discussionmentioning

confidence: 97%

Why Noether’s theorem applies to statistical mechanics

Hermann

Schmidt

2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Noether’s Theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of classical mechanics or on the basis of ﬁeld theory. We have recently shown [Commun. Phys. 4, 176 (2021)] that Noether’s reasoning also applies to thermal systems, where ﬂuctuations are paramount and one aims for a statistical mechanical description. Here we give a pedagogical introduction based on the canonical ensemble and apply it explicitly to ideal sedimentation. The relevant mathematical objects, such as the free energy, are viewed as functionals. This vantage point allows for systematic functional diﬀerentiation and the resulting identities express properties of both macroscopic average forces and molecularly resolved correlations in many-body systems, both in and out-of-equilibrium, and for active Brownian particles. To provide further background, we brieﬂy describe the variational principles of classical density functional theory, of power functional theory, and of classical mechanics.

show abstract