Generalized Boltzmann equation in a manifestly covariant relativistic statistical mechanics
- Tel-Aviv Univ. (Israel)
We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant {open_quotes}historical time{close_quotes} {tau}. We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the H-theorem for evolution in {tau}. In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential V(q), where is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative O(2,1)-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 146084
- Journal Information:
- Foundations of Physics, Journal Name: Foundations of Physics Journal Issue: 9 Vol. 25; ISSN FNDPA4; ISSN 0015-9018
- Country of Publication:
- United States
- Language:
- English
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