URN to cite this document: urn:nbn:de:bvb:703epub70398
Title data
Hermann, Sophie ; Schmidt, Matthias:
Why Noether’s theorem applies to statistical mechanics.
In: Journal of Physics: Condensed Matter.
Vol. 34
(2022)
Issue 21
.
 No. 213001.
ISSN 09538984
DOI der Verlagsversion: https://doi.org/10.1088/1361648X/ac5b47


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Project information
Project financing: 
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 particlebased 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 manybody systems, both in and outofequilibrium, 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.
Further data
Item Type:  Article in a journal 

Keywords:  statistical mechanics; density functional theory; power functional theory;
invariance; Noether’s theorem; liquid state theory; sum rules 
DDC Subjects:  500 Science > 530 Physics 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II > Chair Theoretical Physics II  Univ.Prof. Dr. Matthias Schmidt Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub70398 
Date Deposited:  07 Jul 2023 08:35 
Last Modified:  07 Jul 2023 08:36 
URI:  https://epub.unibayreuth.de/id/eprint/7039 