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Variance of fluctuations from Noether invariance

Title data

Hermann, Sophie ; Schmidt, Matthias:
Variance of fluctuations from Noether invariance.
In: Communications Physics. Vol. 5 (2022) . - 276.
ISSN 2399-3650
DOI: https://doi.org/10.1038/s42005-022-01046-3

Official URL: Volltext

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Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from the irregular motion of thermal degrees of freedom and statistical mechanics facilitates their description. Here we demonstrate that fluctuations are constrained by the inherent symmetries of the given system. For particle-based classical many-body systems, Noether invariance at second order in the symmetry parameter leads to exact sum rules. These identities interrelate the global force variance with the mean potential energy curvature. Noether invariance is restored by an exact balance between these distinct mechanisms. The sum rules provide a practical guide for assessing and constructing theories, for ensuring self-consistency in simulation work, and for providing a systematic pathway to the theoretical quantification of fluctuations.

Further data

Item Type: Article in a journal
Refereed: Yes
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 530 Physics
Date Deposited: 29 Jul 2023 21:00
Last Modified: 19 Mar 2024 08:11
URI: https://eref.uni-bayreuth.de/id/eprint/86409