Quantum-Coherent Thermodynamics: Leaf Typicality via Minimum-Variance Foliation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917467384709120 |
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| author | Fagotti, Maurizio |
| author_facet | Fagotti, Maurizio |
| contents | Equilibrium statistical ensembles commute with the Hamiltonian and thus carry no coherence in the energy eigenbasis. We develop a framework in which energy fluctuations can retain genuinely quantum-coherent contributions. We foliate state space into ``minimum-variance leaves,'' defined by minimizing the average energy variance over all pure-state decompositions, with the minimum set by the quantum Fisher information. On each leaf we construct the least-biased state compatible with normalization and mean energy, defining a leaf-canonical ensemble. The Gibbs ensemble is recovered on the distinguished commuting leaf, while generic states are organized by their leaf label. This structure provides a natural setting to extend eigenstate thermalization beyond equilibrium via a ``leaf typicality'' hypothesis. According to that hypothesis, local observables depend only on the leaf and energy and are reproduced by a representative pure state drawn from the optimal ensemble, whose minimized energy spread reduces the complexity of time evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum-Coherent Thermodynamics: Leaf Typicality via Minimum-Variance Foliation Fagotti, Maurizio Quantum Physics Statistical Mechanics Mathematical Physics Equilibrium statistical ensembles commute with the Hamiltonian and thus carry no coherence in the energy eigenbasis. We develop a framework in which energy fluctuations can retain genuinely quantum-coherent contributions. We foliate state space into ``minimum-variance leaves,'' defined by minimizing the average energy variance over all pure-state decompositions, with the minimum set by the quantum Fisher information. On each leaf we construct the least-biased state compatible with normalization and mean energy, defining a leaf-canonical ensemble. The Gibbs ensemble is recovered on the distinguished commuting leaf, while generic states are organized by their leaf label. This structure provides a natural setting to extend eigenstate thermalization beyond equilibrium via a ``leaf typicality'' hypothesis. According to that hypothesis, local observables depend only on the leaf and energy and are reproduced by a representative pure state drawn from the optimal ensemble, whose minimized energy spread reduces the complexity of time evolution. |
| title | Quantum-Coherent Thermodynamics: Leaf Typicality via Minimum-Variance Foliation |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2602.12212 |