  The role of the algebraic method has long been understood in shedding light
on the topological structure of sets. However, when the set is a simplicial
complex and host to a dynamical process, in particular the trajectory of a
canonically distributed system in thermal equilibrium with a heat bath, the
algebra re-enters. Via a theorem of Levy and Dynkin, there is a correspondence
between a system's energy process at equilibrium and a sequence of $n-$chains
on the state space.
