Dissipation, Generalized Free Energy, and a Self-consistent Nonequilibrium Thermodynamics of Chemically Driven Open Subsystems

摘要

Nonequilibrium thermodynamics of a system situated in a sustained environmentwith influx and efflux is usually treated as a subsystem in a larger, closed"universe". It remains a question what the minimally required description forthe surrounding of such an open driven system is, so that its nonequilibriumthermodynamics can be established solely based on the internal stochastickinetics. We provide a solution to this problem using insights from studies ofmolecular motors in a chemical nonequilibrium steady state (NESS) withsustained external drive through a regenerating system, or in a quasi-steadystate (QSS) with an excess amount of ATP, ADP, and Pi. We introduce the keynotion of {\em minimal work} that is needed, $W_{min}$, for the externalregenerating system to sustain a NESS ({\em e.g.}, maintaining constantconcentrations of ATP, ADP and Pi for a molecular motor). Using a Markov(master-equation) description of a motor protein, we illustrate that the NESSand QSS have identical kinetics as well as the Second Law in terms of a samepositive entropy production rate. The difference between the heat dissipationof a NESS and its corresponding QSS is exactly the $W_{min}$. This provides ajustification for introducing an {\em ideal external regenerating system} andyields a {\em free energy balance equation} between the net free energy input$F_{in}$ and total dissipation $F_{dis}$ in an NESS: $F_{in}$ consists ofchemical input minus mechanical output; $F_{dis}$ consists of dissipative heat;and the amount of useful energy becoming heat is the NESS entropy production.Furthermore, we show that for non-stationary systems, the $F_{dis}$ and$F_{in}$ correspond to the entropy production rate and housekeeping heat instochastic thermodynamics, and identify a relative entropy $H$ as a generalizedfree energy.