Relativistic classical and quantum statistical mechanics and covariant boltzmann equation

In this chapter, we shall discuss the statistical mechanics of a many event system, for which the points in space time constitute the fundamental entities for which distribution functions must be constructed to achieve a manifestly covariant theory. Assuming that each event is part of an evolving world line, as in our construction of Chap. 4. the counting of events is essentially equivalent to the counting of world lines corresponding to particles. Therefore one should expect that, as we indeed find, the statistical mechanics of events is closely related to the theory of statistical mechanics of particles, as developed, for example, in Synge (1957); see also, de Groot (1980). Hakim (2011), Israel and Kandrup (1984) stress the importance of manifest covariance. We construct a canonical Gibbs ensemble based on a microcanonical ensemble, as is usual in statistical mechanics (e.g. Huang 1967), enabling us to define a temperature and the basic thermodynamic functions (Horwitz 1981).