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Noether’s theorem in statistical mechanics

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006036
URN to cite this document: urn:nbn:de:bvb:703-epub-6036-2

Title data

Hermann, Sophie ; Schmidt, Matthias:
Noether’s theorem in statistical mechanics.
In: Communications Physics. Vol. 4 (2021) Issue 1 . - No. 176.
ISSN 2399-3650
DOI der Verlagsversion: https://doi.org/10.1038/s42005-021-00669-2

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Abstract

Noether’s calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy and the power functional, for equilibrium and driven many-body systems. Translational and rotational symmetry operations yield mechanical laws. These global identities express vanishing of total internal and total external forces and torques. We show that functional differentiation then leads to hierarchies of local sum rules that interrelate density correlators as well as static and time direct correlation functions, including memory. For anisotropic particles, orbital and spin motion become systematically coupled. The theory allows us to shed new light on the spatio-temporal coupling of correlations in complex systems. As applications we consider active Brownian particles, where the theory clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation, the center-of-mass motion is constrained by an internal Noether sum rule.

Further data

Item Type: Article in a journal
Keywords: Condensed-matter physics; Statistical physics
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:703-epub-6036-2
Date Deposited: 14 Mar 2022 10:19
Last Modified: 15 Mar 2022 05:55
URI: https://epub.uni-bayreuth.de/id/eprint/6036

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