Approach to equilibrium of a relativistic gas (Q1062238)

Serious studies on relativistic gas, especially its equilibrium properties have always been of great interest. Here the author deals with the global behaviour of a gas in a purely gravitational field. Working within the kinetic theory and stationary space-time, it is demonstrated that the entropy may not grow indefinitely. The approach of a gas steadily to equilibrium is taken as one of the consequences of this assertion. Defining a special function H(t) which contains most of the information about the state of the gas, its estimates are given. Also making use of equi-measurable functions the main problem of the paper is solved by evaluating the integral of entropy in question.