Geometric decomposition of entropy production in stochastic and chemical systems

Entropy production is central to understanding nonequilibrium phenomena. It is known that decomposing entropy production enables us to separately treat distinct two aspects of dynamics, nonstationarity and breaking of detailed balance. In this seminar, I talk about our recent progress on geometric decomposition of entropy production in discrete stochastic systems and deterministic chemical systems. For the audience who may not be familiar with nonequilibrium thermodynamics and linear algebraic graph theory, which the latter enables us to treat the two kinds of systems at once, I would like to start with a very basic introduction. Then I explain why and how we decompose entropy production. Specifically, I mainly focus on the "Onsager-projective decomposition" we study in arXiv:2205.15227 rather than the information geometric decomposition provided in the following paper arXiv:2206.14599. Further, several physical consequences will be discussed, including generalization of Schnakenberg's decomposition stemming from cycles in a steady system, and its relation to gradient flow expressions of a master equation and a rate equation.