Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915969304100864 |
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| author | Jiang, Chunlan Wan, Jincheng Wu, Jinsong |
| author_facet | Jiang, Chunlan Wan, Jincheng Wu, Jinsong |
| contents | The bimodule KMS symmetry of a bimodule quantum Markov semigroup extends the classical KMS symmetry of a quantum Markov semigroup. Compared with (bimodule) GNS symmetry, the (bimodule) KMS symmetry retains significantly more of the underlying noncommutativity. In this paper, we study bimodule KMS symmetric quantum Markov semigroups and introduce directional matrices for such semigroups, which reduce to diagonal matrices in the GNS symmetric setting. Using these directional matrices, we establish a corresponding gradient-flow structure. As a consequence, we obtain both a modified logarithmic Sobolev inequality and a Talagrand inequality for bimodule KMS symmetric quantum Markov semigroups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows Jiang, Chunlan Wan, Jincheng Wu, Jinsong Operator Algebras Functional Analysis 46L57, 46L37, 46L67, 81S22 The bimodule KMS symmetry of a bimodule quantum Markov semigroup extends the classical KMS symmetry of a quantum Markov semigroup. Compared with (bimodule) GNS symmetry, the (bimodule) KMS symmetry retains significantly more of the underlying noncommutativity. In this paper, we study bimodule KMS symmetric quantum Markov semigroups and introduce directional matrices for such semigroups, which reduce to diagonal matrices in the GNS symmetric setting. Using these directional matrices, we establish a corresponding gradient-flow structure. As a consequence, we obtain both a modified logarithmic Sobolev inequality and a Talagrand inequality for bimodule KMS symmetric quantum Markov semigroups. |
| title | Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows |
| topic | Operator Algebras Functional Analysis 46L57, 46L37, 46L67, 81S22 |
| url | https://arxiv.org/abs/2511.04881 |