Information geometry of excess and housekeeping entropy production

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.