Housekeeping and excess entropy production for general nonlinear dynamics

We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in discrete space, including chemical reaction networks and stochastic systems. exploit the geometric structure thermodynamic forces to define decomposition; this does not rely on notion steady state, it even applies systems that exhibit multistability, limit cycles, chaos. In decomposition, distinct aspects contribute separately production: housekeeping part stems from cyclic mode arises external driving, generalizing Schnakenberg's nonsteady states, while excess an instantaneous relaxation conservative forces. Our refines previously known uncertainty relations speed limits. particular, only improves optimal-transport-theoretic limit, but also extends optimal transport theory nonconservative settings.