Noether-Constrained Correlations in Equilibrium Liquids

Abstract

Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field the Noether theorem yields the local force balance. Three distinct two-body correlation functions emerge at second order, namely the standard two-body density, the localized force-force correlation function, and the localized force gradient. An exact Noether sum rule interrelates these correlators. Simulations of Lennard-Jones, Yukawa, soft-sphere dipolar, Stockmayer, Gay-Berne and Weeks-Chandler-Andersen liquids, of monatomic water and of a colloidal gel former demonstrate their fundamental role in the characterization of spatial structure.

Previous title was: "What is liquid, from Noether's perspective?"

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• Active crystallization from power functional theory
• First part of Clausius heat theorem in terms of Noether's theorem
• Metadensity functional learning for classical fluids: Regularizing with pair correlations