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Why Noether’s theorem applies to statistical mechanics

Titelangaben

Hermann, Sophie ; Schmidt, Matthias:
Why Noether’s theorem applies to statistical mechanics.
In: Journal of Physics: Condensed Matter. Bd. 34 (2022) Heft 21 . - 213001.
ISSN 1361-648X
DOI: https://doi.org/10.1088/1361-648X/ac5b47

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Projektfinanzierung: Deutsche Forschungsgemeinschaft

Abstract

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 (2021 Commun. Phys. 4 176) 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.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: statistical mechanics; density functional theory; power functional theory;
invariance; Noether’s theorem; liquid state theory; sum rules
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Physikalisches Institut > Lehrstuhl Theoretische Physik II > Lehrstuhl Theoretische Physik II - Univ.-Prof. Dr. Matthias Schmidt
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Physikalisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Physikalisches Institut > Lehrstuhl Theoretische Physik II
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Eingestellt am: 08 Jul 2023 21:00
Letzte Änderung: 06 Mai 2024 13:34
URI: https://eref.uni-bayreuth.de/id/eprint/86062