Hybrid quantum-classical systems: Statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble

Alonso, J. L. (Universidad de Zaragoza) ; Bouthelier-Madre, C. ; Castro, A. ; Clemente-Gallardo, J. (Universidad de Zaragoza) ; Jover-Galtier, J. A. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1103/kjdp-1g12

Año: 2026

Publicado en: Physical Review E 113, 3 (2026), [16 pp.]
ISSN: 2470-0045

Financiación: info:eu-repo/grantAgreement/ES/AEI/CPP2021-008644
Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00
Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-123251NB-I00
Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)
Área (Departamento): Área Física Teórica (Dpto. Física Teórica)