Information geometry of excess and housekeeping entropy production

Abstract

A nonequilibrium system is characterized by a set of thermodynamic forces and fluxes, which give rise to entropy production (EP). We demonstrate that these forces and fluxes have an information-geometric structure, which allows us to decompose EP into nonnegative contributions from different types of forces. We focus on the excess and housekeeping decomposition, which reflects contributions from conservative and nonconservative forces, in the general setting of discrete systems (linear master equations and nonlinear chemical dynamics). Unlike the nonadiabatic/adiabatic (Hatano-Sasa) approach, our decomposition is always well-defined, including in systems with odd variables and nonlinear systems without steady states. It is also operationally meaningful, leading to far-from-equilibrium thermodynamic uncertainty relations and speed limits.

Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport

“…This projection theorem for the excess entropy production rate was substantially obtained in Ref. [44] for the general Markov process. This result also gives another link between information geometry in the space of path probability densities and optimal transport theory.…”

“…For example, generalizations of the results in this paper for the master equation have been seen in Refs. [22,25,28,38,41,43,44,60,76]. Because generalizations are not unique, rather different approaches of optimal transport theory for stochastic thermodynamics in the Markov jump process have also been seen in Refs.…”

“…[77][78][79][80]. Unlike these generalizations, our generalizations [43,44] are related to the gradient flow expression and information-geometric projection discussed in this paper. The generalization for the deterministic chemical rate equation is also interesting to consider information geometry and optimal transport theory for chemical thermodynamics, which was proposed in Refs.…”

“…The generalization for the deterministic chemical rate equation is also interesting to consider information geometry and optimal transport theory for chemical thermodynamics, which was proposed in Refs. [29,[42][43][44][80][81][82][83]. For the deterministic chemical rate equation, we do not need to use stochasticity to obtain generalized results, and geometric properties play a crucial role in the derivation of generalized results, similarly as in the stochastic case.…”

“…In this paper, we summarize our recent development of differential geometry for non-equilibrium thermodynamics [22,24,25,29,31,[37][38][39][40][41][42][43][44][45] and propose several relations between these studies by focusing on non-equilibrium dynamics of the Fokker-Planck equation. Because entropy production for the Fokker-Planck equation can be discussed from the viewpoint of both information geometry and optimal transport theory, these relations provide links between information geometry and optimal transport theory.…”