Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals
Anno: 2011
Autori: Franzosi R.
Affiliazione autori: C.N.I.S.M. UdR di Firenze, Dipartimento di Fisica, Università degli Studi di Firenze, Via Sansone 1, 50019, Sesto Fiorentino, Italy; I.P.S.I.A. C. Cennini, Via dei Mille 12/a, 53034, Colle di Val d’Elsa (SI), Italy
Abstract: We consider a generic classical many particle system described by an autonomous Hamiltonian H(x(1), … , x(N+2)) which, in addition, has a conserved quantity V (x(1), … , x(N+2)) = v, so that the Poisson bracket {H, V} vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over sub-manifolds given by the intersection of the constant energy hyper-surfaces with those defined by V (x(1), … , x(N+2)) = v. We show that temperature and higher order derivatives of entropy are microcanonical observable that, under the hypothesis of ergodicity, can be calculated as time averages of suitable functions. We derive the explicit expression of the function that gives the temperature.
Giornale/Rivista: JOURNAL OF STATISTICAL PHYSICS
Volume: 143 (4) Da Pagina: 824 A: 830
Parole chiavi: Statisical Mechanics; Differential Geometry; DOI: 10.1007/s10955-011-0200-4Citazioni: 21dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui
