Hybrid quantum-classical dynamics with stationary thermal states

Quantum Physics [Submitted on 2 Apr 2026] Hybrid quantum-classical dynamics with stationary thermal states Adrián A. Budini Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is, a density matrix that maximizes the hybrid arrangement entropy under the constraints of a canonical ensemble. Introducing a detailed balance condition, it is found that a specific subclass of hybrid Lindblad equations fulfill the demanded requirement. The main theoretical results are exemplified through a set of specific examples that in addition lighten how the thermal state of each subsystem in isolation is affected by their mutual coupling. In particular, a Gaussian thermal state could become a bimodal distribution when increasing the interaction strength of a classical subsystem with a quantum two-level subsystem. Comments: 11 pages, 2 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02484 [quant-ph]   (or arXiv:2604.02484v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02484 Focus to learn more Submission history From: Adrian Budini [view email] [v1] Thu, 2 Apr 2026 19:36:19 UTC (249 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)