Geometric Microcanonical Thermodynamics for Systems with First Integrals

Abstract

In the general case of a many-body Hamiltonian system, described by an autonomous Hamiltonian $H$, and with $K\ge 0$ independent conserved quantities, we derive the microcanonical thermodynamics. By a simple approach, based on the 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, as the temperature, the chemical potential or 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 non-separable Hamiltonians, where the usual definition of kinetic temperature, derived by the virial theorem, does not apply.

4 pages

References in corpus (4)

• Microcanonical temperature for a classical field: application to Bose-Einstein condensation
• Topology and Phase Transitions II. Theorem on a necessary relation
• Topology and Phase Transitions I. Preliminary Results
• Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals

Cited by in corpus (6)

• Statistical Mechanics of Systems with Negative Temperature
• On the dispute between Boltzmann and Gibbs entropy
• Phase transitions at high energy vindicate negative microcanonical temperature
• Geometrical aspects in the analysis of microcanonical phase-transitions
• Microcanonical entropy for classical systems
• A microcanonical entropy correcting finite-size effects in small systems