Geometric microcanonical thermodynamics for systems with first integrals

Year: 2012

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.


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, Hamiltonians
DOI: 10.1103/PhysRevE.85.050101

Citations: 7
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