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.