  From a conceptual point of view, the transition from kinetic gas theory to statistical mechanics poses two main foundational questions. On what grounds do we choose a particular ensemble, or the probability distribution characterizing the system? Gibbs did not enter into a systematic discussion of this problem, but only discussed special cases of equilibrium ensembles (i.e. canonical, micro-canonical etc.). A second problem is to relate the ensemble-based probabilities with the probabilities obtained in the earlier kinetic approach for a single gas model.