SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Statistical Physics: General I

DY 6.1: Vortrag

Montag, 27. März 2023, 10:00–10:15, ZEU 160

Noether's theorem in statistical mechanics — •Sophie Hermann and Matthias Schmidt — Universität Bayreuth, Bayreuth, Deutschland

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 apply Noether's calculus of invariant variations to thermal systems, where fluctuations are paramount and one aims for a statistical mechanical description, both in and out of equilibrium. Generating functionals, such as the free energy, yield mechanical laws under continuous translational and rotational symmetry operations. The resulting global theorems express vanishing of total internal and total external forces and torques. Local sum rules interrelate density correlators, as well as static and time direct correlation functions via infinite hierarchies, including memory. We demonstrate that this approach is consistent with the earlier work in equilibrium, and that it enables one to go, with relative ease, beyond the sum rules that these authors formulated. For anisotropic particles, systematic coupling of orbital and spin motion is identified. The theory allows to shed new light on the spatio-temporal coupling of correlations in complex systems. We present novel exact and nontrivial identities that apply to time-dependent problems and driven and active fluids.