Direct Interactions in Relativistic Statistical Mechanics
Ph. Droz-Vincent (CNRS, Universit\'e P. et M. Curie, Paris)
TL;DR
This paper explores the properties of directly interacting particles within relativistic mechanics, focusing on phase invariance, conserved quantities, and equilibrium concepts in a multitime formalism.
Contribution
It introduces a covariant framework for analyzing direct interactions in relativistic systems and discusses conservation laws and equilibrium definitions.
Findings
Phase average of first integrals is conserved under invariant phase-space volume
Hamiltonian models exhibit specific conservation properties
A tentative equilibrium definition is proposed
Abstract
Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral, covariantly defined as a flux across a -dimensional surface, is conserved. The Hamiltonian case is discussed, a class of simple models is exhibited, and a tentative definition of equilibrium is proposed.
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