## 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 0953-8984

DOI: https://doi.org/10.1088/1361-648X/ac5b47

## Project information

Project financing: |
Deutsche Forschungsgemeinschaft |
---|

## Abstract in another language

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.

## Further data

Item Type: | Article in a journal |
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Refereed: | Yes |

Keywords: | statistical mechanics; density functional theory; power functional theory; invariance; Noether’s theorem; liquid state theory; sum rules |

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: | 08 Jul 2023 21:00 |

Last Modified: | 10 Jul 2023 04:59 |

URI: | https://eref.uni-bayreuth.de/id/eprint/86062 |