  The capabilities of a new approach towards the foundations of Statistical
Mechanics are explored. The approach is genuine quantum in the sense that
statistical behavior is a consequence of objective quantum uncertainties due to
entanglement and uncertainty relations. No additional randomness is added by
hand and no assumptions about a priori probabilities are made, instead measure
concentration results are used to justify the methods of Statistical Physics.
The approach explains the applicability of the microcanonical and canonical
ensemble and the tendency to equilibrate in a natural way. This work contains a
pedagogical review of the existing literature and some new results. The most
important of which are: i) A measure theoretic justification for the
microcanonical ensemble. ii) Bounds on the subsystem equilibration time. iii) A
proof that a generic weak interaction causes decoherence in the energy
eigenbasis. iv) A proof of a quantum H-Theorem. v) New estimates of the average
effective dimension for initial product states and states from the mean energy
ensemble. vi) A proof that time and ensemble averages of observables are
typically close to each other. vii) A bound on the fluctuations of the purity
of a system coupled to a bath.
