Thermodynamics in Terms of a Sequence of $n-$chains Derived from a Martingale Decomposition of the Energy Process

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107132The 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.8 pages, 3 figuresStatistical MechanicsOther Condensed MatterMathematical PhysicsData Analysis, Statistics and ProbabilityThermodynamics in Terms of a Sequence of $n-$chains Derived from a Martingale Decomposition of the Energy Processtext