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DY: Fachverband Dynamik und Statistische Physik
DY 5: Statistical Physics: General
DY 5.6: Vortrag
Montag, 17. März 2025, 10:45–11:00, H47
Noether-constrained correlations and hyperforces in equilibrium liquids — •Sophie Hermann1,2, Silas Robitschko1, Florian Sammüller1, and Matthias Schmidt1 — 1Universität Bayreuth, Bayreuth, Germany — 2Sorbonne Université/CNRS, Paris, France
Noether’s calculus of invariant variations in statistical mechanics yields exact identities (“sum rules”) from functional symmetries. The invariance of spatial transformation of the underlying classical many-body Hamiltonian at first order in the transformation field Noether’s theorem yields the local force balance. At second order three distinct two-body correlation functions emerge, 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. More generally exploiting invariance of a thermally averaged classical phase space functions results in hyperforce sum rules. These relate the mean gradient of a phase-space function to its negative mean product with the total force. As applications we investigate via computer simulations (including Lennard-Jones liquids, monatomic water and a colloidal gel former) the emerging one-body force fluctuation profiles in bulk and confined liquids. These local correlators quantify spatially inhomogeneous self-organization, demonstrate their fundamental role in the characterization of spatial structure and their measurement allows for the development of stringent convergence tests and enhanced sampling schemes in complex systems.
Keywords: Noether's Theorem; (Hyper-) Forces; Exact Identities; Sum Rules