  The first objective of this article is to show that the black hole partition
function can be placed on a firm logical foundation by enclosing the black hole
in a spatially finite "box" or boundary. The presence of the box has the effect
of stabilizing the black hole and yields a system with a positive heat
capacity. The second objective of this article is to explore the origin of
black hole entropy. This is accomplished through the construction of a path
integral expression for the density matrix for the gravitational field, and
through an analysis of the connection between the density matrix and the black
hole density of states. Our results suggest that black hole entropy can be
associated with an absence of certain "inner boundary information" for the
system. (Based on the talk presented by J.D. Brown at the conference "The Black
Hole 25 Years After", Santiago, Chile, January 1994.)
