Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals
Year: 2011
Authors: Franzosi R.
Autors Affiliation: 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.
Journal/Review: JOURNAL OF STATISTICAL PHYSICS
Volume: 143 (4) Pages from: 824 to: 830
KeyWords: Statisical Mechanics; Differential Geometry; DOI: 10.1007/s10955-011-0200-4ImpactFactor: 1.397Citations: 21data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here
