Intertwining Markov Processes via Matrix Product Operators
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916015166717952 |
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| author | Frassek, Rouven de Gier, Jan Li, Jimin Verstraete, Frank |
| author_facet | Frassek, Rouven de Gier, Jan Li, Jimin Verstraete, Frank |
| contents | Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement duality transformations in one-dimensional boundary-driven Markov processes on lattices. In contrast to local dualities associated with generalised symmetries, here the duality operator intertwines two Markov processes via generalised exchange relations and realises the out-of-equilibrium duality globally. We construct these operators exactly for the symmetric simple exclusion process with distinct out-of-equilibrium boundaries. In this case, out-of-equilibrium boundaries are dual to equilibrium boundaries satisfying Liggett's condition, implying that the Gibbs-Boltzmann measure captures out-of-equilibrium physics when leveraging the duality operator. We illustrate this principle through physical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09928 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intertwining Markov Processes via Matrix Product Operators Frassek, Rouven de Gier, Jan Li, Jimin Verstraete, Frank Mathematical Physics Statistical Mechanics Exactly Solvable and Integrable Systems Quantum Physics Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement duality transformations in one-dimensional boundary-driven Markov processes on lattices. In contrast to local dualities associated with generalised symmetries, here the duality operator intertwines two Markov processes via generalised exchange relations and realises the out-of-equilibrium duality globally. We construct these operators exactly for the symmetric simple exclusion process with distinct out-of-equilibrium boundaries. In this case, out-of-equilibrium boundaries are dual to equilibrium boundaries satisfying Liggett's condition, implying that the Gibbs-Boltzmann measure captures out-of-equilibrium physics when leveraging the duality operator. We illustrate this principle through physical applications. |
| title | Intertwining Markov Processes via Matrix Product Operators |
| topic | Mathematical Physics Statistical Mechanics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2603.09928 |