170025 20260316092629.0 doi 10.1103/kjdp-1g12 sideral 148576 ART-2026-148576 eng Alonso, J. L. Universidad de Zaragoza (orcid)0000-0003-0694-155X Hybrid quantum-classical systems: Statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble 2026 We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of hybrid systems. We investigate its properties, and in particular how the microcanonical ensemble and its marginal classical and quantum ensembles can be defined for arbitrarily small range of energies for the whole system. We show how, in this situation, the ensembles are well defined for a continuum of energy values, unlike the purely quantum microcanonical ensemble, thus proving that hybrid systems translate properties of classical systems to the quantum realm. We also analyze the relation with the hybrid canonical ensemble by considering the microcanonical ensemble of a compound system composed of a hybrid subsystem weakly coupled to a reservoir and computing the marginal ensemble of the hybrid subsystem. Lastly, we apply the theory to the statistics of a toy model, which gives some insight on the different properties presented along the article. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/AEI/CPP2021-008644 info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00 info:eu-repo/grantAgreement/ES/AEI/PID2021-123251NB-I00 info:eu-repo/grantAgreement/ES/DGA/E24-23R info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Bouthelier-Madre, C. (orcid)0000-0003-1697-5710 Castro, A. (orcid)0000-0002-9253-7926 Clemente-Gallardo, J. Universidad de Zaragoza (orcid)0000-0003-4721-7381 Jover-Galtier, J. A. Universidad de Zaragoza (orcid)0000-0001-9868-9368 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 113, 3 (2026), [16 pp.] Phys. rev., E Physical Review E 2470-0045 531546 http://zaguan.unizar.es/record/170025/files/texto_completo.pdf Postprint 3107310 http://zaguan.unizar.es/record/170025/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:170025 articulos driver 2026-03-16-08:17:03 ARTICLE