There are two distinct approaches for deriving the canonical ensemble. The canonical ensemble either follows
as a special limit of the microcanonical ensemble or alternatively follows from the maximum entropy principle.
We show the equivalence of these two approaches by applying the maximum entropy formulation to a closed
universe consisting of an open system plus bath. We show that the target function for deriving the canonical
distribution emerges as a natural consequence of partial maximization of the entropy over the bath degrees
of freedom alone. By extending this mathematical formalism to dynamical paths rather than equilibrium
ensembles, the result provides an alternative justification for the principle of path entropy maximization
as well.