In this paper, a start is made toward the development of a statistical mechanics that will be suited to the treatment of dynamic changes in thermodynamic systems and which, at the same time, will be in the appropriate form for a relativistically invariant theory. The formal device consists of making the time coordinate one of the canonical variables. As a result, stationary ensembles no longer occupy a privileged position among all conceivable Gibbs ensembles, and it becomes necessary to redefine and to reformulate most statistical and thermodynamic concepts. This has been done with the concept of a canonical ensemble, with entropy, temperature, heat flux, and performance of work. With a suitable definition of the entropy of an individual system, a new formulation of the $H$-theorem is provided, which in turn leads to a formulation of the Second Law.