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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2510.02888 |
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| _version_ | 1866918153726984192 |
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| author | Duvenhage, Rocco van Zyl, Dylan Zurlo, Paola |
| author_facet | Duvenhage, Rocco van Zyl, Dylan Zurlo, Paola |
| contents | Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded transport plans, on usual and fermionic (or $\mathbb{Z}_2$-graded) tensor products respectively. The metric properties of these fermionic Wasserstein distances are shown, and their symmetries relevant to deviation of a system from quantum detailed balance are investigated. The latter is done in conjunction with the development of a complete mathematical framework for detailed balance in systems involving indistinguishable fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fermionic optimal transport Duvenhage, Rocco van Zyl, Dylan Zurlo, Paola Mathematical Physics Operator Algebras Quantum Physics Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded transport plans, on usual and fermionic (or $\mathbb{Z}_2$-graded) tensor products respectively. The metric properties of these fermionic Wasserstein distances are shown, and their symmetries relevant to deviation of a system from quantum detailed balance are investigated. The latter is done in conjunction with the development of a complete mathematical framework for detailed balance in systems involving indistinguishable fermions. |
| title | Fermionic optimal transport |
| topic | Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2510.02888 |