Geometric microcanonical thermodynamics for systems with first integrals
Authors: Franzosi R.
Autors Affiliation: CNR, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
Abstract: In the general case of a many-body Hamiltonian system described by an autonomous Hamiltonian H and with K >= 0 independent conserved quantities, we derive the microcanonical thermodynamics. Using simple approach, based on differential geometry, we derive the microcanonical entropy and the derivatives of the entropy with respect to the conserved quantities. In such a way, we show that all the thermodynamical quantities, such as the temperature, the chemical potential, and the specific heat, are measured as a microcanonical average of the appropriate microscopic dynamical functions that we have explicitly derived. Our method applies also in the case of nonseparable Hamiltonians, where the usual definition of kinetic temperature, derived by the virial theorem, does not apply.
Journal/Review: PHYSICAL REVIEW E
Volume: 85 (5.1) Pages from: 050101 to: 050101
KeyWords: Conserved quantity; Differential geometry; First integral; Hamiltonian systems; Kinetic temperatures; Many-body; Microcanonical entropy; Microcanonical thermodynamics; Nonseparable; Simple approach; Thermodynamical quantities; Virial theorems, Entropy; Thermodynamics, HamiltoniansDOI: 10.1103/PhysRevE.85.050101Citations: 7data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2022-01-16References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here