Gauge Invariance of Equilibrium Statistical Mechanics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916487607877632 |
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| author | Müller, Johanna Hermann, Sophie Sammüller, Florian Schmidt, Matthias |
| author_facet | Müller, Johanna Hermann, Sophie Sammüller, Florian Schmidt, Matthias |
| contents | We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra, which induces exact sum rules when thermally averaged. Gauge invariance with respect to finite shifting is demonstrated via Monte Carlo simulation in the transformed phase space which generates identical equilibrium averages. Our results point towards a deeper basis of statistical mechanics than previously known and they offer avenues for systematic construction of exact identities and of sampling algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauge Invariance of Equilibrium Statistical Mechanics Müller, Johanna Hermann, Sophie Sammüller, Florian Schmidt, Matthias Statistical Mechanics Soft Condensed Matter We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra, which induces exact sum rules when thermally averaged. Gauge invariance with respect to finite shifting is demonstrated via Monte Carlo simulation in the transformed phase space which generates identical equilibrium averages. Our results point towards a deeper basis of statistical mechanics than previously known and they offer avenues for systematic construction of exact identities and of sampling algorithms. |
| title | Gauge Invariance of Equilibrium Statistical Mechanics |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2406.19235 |