  We characterize the classical Boltzmann distribution as the unique solution
to a certain combinatorial Hodge theory problem in homological degree zero on a
finite graph. By substituting for the graph a CW complex and a degree d, we are
able to define, by direct analogy, a higher dimensional Boltzmann distribution
as a certain (d-1)-cycle on the real cellular chain complex which is
characterized by appropriate constraints. We then give an explicit formula for
this cycle. We explain how this circle of ideas relates to the authors' Higher
Kirchhoff Network Theorem. We also give an improved version of the authors'
Higher Matrix-Tree Theorems.
