Noether-Constrained Correlations in Equilibrium Liquids

TL;DR

This paper reveals how Noether's theorem constrains liquid structure through specific correlation functions, connecting thermal invariance to measurable spatial correlations in various liquids.

Contribution

It introduces a novel theoretical framework linking Noether invariants to liquid correlations and validates it with extensive simulations across different liquid models.

Findings

Derivation of three key two-body correlation functions from Noether's theorem.

Establishment of an exact sum rule relating these correlators.

Demonstration of the framework's applicability to diverse liquid systems.

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.