Senior Honors Thesis Presentation: "Cycles, Entropy, and Probability: Markov Chain Thermodynamics"

Speaker: Collin Szczepanski, Washington University in Saint Louis

Abstract: Given a continuous time Markov process on a discrete state space, one can apply the well-established framework of stochastic thermodynamics, a useful example of thermodynamic universality. The process is placed on a graph, whereby the structure of the graph as a topological and geometric object provide insight into the nature of the underlying process. In particular, it is shown how information-theoretic entropy production in the asymptotic time limit is dependent on the Cohomology of the graph. Moreover, the discrete Hodge Laplacian is used to decompose discrete differential forms pertaining to the process. A minimal covering graph is constructed for such forms, the smallest domain where the lifted forms become exact. Through this construction, one can find a thermodynamic potential for the lift of any homogenous Markov process. Further comments are made on the application of results to Markov systems with periodic coefficients, solvable through Floquet theory.

Host: Renato Feres