Abstract
Starting from predictive relativistic mechanics we develop a classical relativistic statistical mechanics. For a system of $N$ particles, the basic distribution function depends, in addition to the $6N$ coordinates and velocities, on $N$ times, instead of a single one as in the usual statistical mechanics. This generalized distribution function obeys $N$ (instead of 1) continuity equations, which give rise to $N$ Liouville equations in the case of a dilute plasma (i.e., to lowest, nonzero order in the charges). Hence, the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the reduced generalized distribution functions is derived. A relativistic Vlasov equation is obtained in this way. Thermal equilibrium is then considered for a dilute plasma. The calculation is explicitly worked out for a weakly relativistic plasma, up to order $\frac{1}{{c}^{2}}$, and known results are recovered.
Highlights
The lack of a classical relativistic theory of interacting particles for many years has had as a consequence that a satisfactory classical relativistic statistical This situation mechanics has been does not emphasized exist by Haatvparse. s'ent.in the last few years a consistent framework for classical relativistic systems of interacting particles has been developed
Starting from predictive relativistic mechanics we develop a classical relativistic statistical mechanics
The original work is in Refs. 2-5, and in Ref. 4 this new framework has been called "predictive relativistic mechanics" (PRM)
Summary
Departamento de Fs'sica Teorica, Universidad de Santander, Spain (Received 24 June 1980). For a system of N particles, the basic distribution function depends, in addition to the 6 N coordinates and velocities, on N times, instead of a single one as in the usual statistical mechanics. This generalized distribution function obeys N (instead of 1) continuity equations, which give rise to N Liouville equations in the case of a dilute plasma (i.e., to lowest, nonzero order in the charges). The Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the reduced generalized distribution functions is derived. The calculation is explicitly worked out for a weakly relativistic plasma, up to order 1/c', and known results are recovered
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