Coarse-Graining Chemical Networks by Trimming to Preserve Energy Dissipation

Continuous production of entropy and the corresponding energy dissipation is a defining characteristic of nonequilibrium systems. When a system’s full chemical kinetic description is known, its entropy production rate can be computed from the microscopic rate constants. However, such a calculation typically underestimates energy dissipation when the states of the underlying system are mesoscopic, i.e., when they combine multiple microscopic states, a situation typical in experimental measurements with finite resolution. It is unknown whether there is a mesoscopic coarse-graining procedure that produces fewer states but allows for precise entropy production calculations. Here we develop a universal coarse-graining procedure that we call “trimming”, in which microscopic states of the original Markov network are progressively eliminated but the fluxes between remaining states are exactly preserved. We demonstrate that this procedure also preserves entropy production as long as no dissipative loops are eliminated. We apply our method to several examples illustrating how trimming affects local network topology.