000078899 001__ 78899 000078899 005__ 20190508155154.0 000078899 0247_ $$2doi$$a10.1088/1751-8113/44/39/395004 000078899 0248_ $$2sideral$$a73909 000078899 037__ $$aART-2011-73909 000078899 041__ $$aspa 000078899 100__ $$0(orcid)0000-0003-0694-155X$$aAlonso, J.L.$$uUniversidad de Zaragoza 000078899 245__ $$aStatistics and Nos\'e formalism for Ehrenfest dynamics 000078899 260__ $$c2011 000078899 5060_ $$aAccess copy available to the general public$$fUnrestricted 000078899 5203_ $$aQuantum dynamics (i.e. the Schrödinger equation) and classical dynamics (i.e. Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper, we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well-defined Poisson bracket allows us to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of an Ehrenfest system, it is straightforward to extend the formalism of Nosé (invented to do constant temperature molecular dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics. 000078899 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/DGA/E24-2$$9info:eu-repo/grantAgreement/ES/DGA/E24-3$$9info:eu-repo/grantAgreement/ES/MICINN/FIS2009-13364-C02-01$$9info:eu-repo/grantAgreement/ES/MICINN/FPA2009-09638 000078899 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000078899 590__ $$a1.564$$b2011 000078899 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b24 / 84 = 0.286$$c2011$$dQ2$$eT1 000078899 591__ $$aPHYSICS, MATHEMATICAL$$b16 / 55 = 0.291$$c2011$$dQ2$$eT1 000078899 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000078899 700__ $$aCastro, A. 000078899 700__ $$0(orcid)0000-0003-4721-7381$$aClemente-Gallardo, J.$$uUniversidad de Zaragoza 000078899 700__ $$aCuchi, J.C. 000078899 700__ $$0(orcid)0000-0001-8549-3139$$aEchenique, P.$$uUniversidad de Zaragoza 000078899 700__ $$0(orcid)0000-0002-0882-0463$$aFalceto, F.$$uUniversidad de Zaragoza 000078899 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000078899 773__ $$g44, 39 (2011), 395004$$pJournal of Physics A-Mathematical and Theoretical$$tJournal of Physics A-Mathematical and Theoretical$$x1751-8113 000078899 8564_ $$s456466$$uhttps://zaguan.unizar.es/record/78899/files/texto_completo.pdf$$yPostprint 000078899 8564_ $$s29474$$uhttps://zaguan.unizar.es/record/78899/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000078899 909CO $$ooai:zaguan.unizar.es:78899$$particulos$$pdriver 000078899 951__ $$a2019-05-08-14:41:00 000078899 980__ $$aARTICLE