Remarks on Relativistic Statistical Mechanics. I

Abstract

The modifications introduced by the specific forms of relativistic dynamics of many-particle systems are shown to give rise to a different (with respect to the nonrelativistic case) manner to set the problems involved in a tentative construction of relativistic statistical mechanics. Although the difficult problems of relativistic dynamics are not solved, it is possible to define relativistic generalizations of phase space, distribution functions, Gibbs ensembles, and average values. In particular, phase space is chosen for convenience and is no longer related (as is usually the case) to the ``initial data,'' whose nature is yet unknown. As a consequence, only those observables which depend on the variables characterizing phase space give rise to easily computed average values. However, it is possible to enlarge at will the basic phase space and to define subsequent densities from which average values may be calculated. [Example: The calculation of average values of observables A(…xiμ,uiμ…) needs only densities of the form N(…xiμ,uiμ…) and observables involving acceleration variables need the enlarging of phase space so as to include the latter. On this enlarged phase space, densities of the form N(…xiμ,uiμ,γiμ…) may be defined and are used to compute average values, etc.] The notion of equilibrium is discussed and suggestions for reaching the solution of this unsolved problem are made.