  Nonequilibrium thermodynamics of a system situated in a sustained environment
with influx and efflux is usually treated as a subsystem in a larger, closed
"universe". It remains a question what the minimally required description for
the surrounding of such an open driven system is, so that its nonequilibrium
thermodynamics can be established solely based on the internal stochastic
kinetics. We provide a solution to this problem using insights from studies of
molecular motors in a chemical nonequilibrium steady state (NESS) with
sustained external drive through a regenerating system, or in a quasi-steady
state (QSS) with an excess amount of ATP, ADP, and Pi. We introduce the key
notion of {\em minimal work} that is needed, $W_{min}$, for the external
regenerating system to sustain a NESS ({\em e.g.}, maintaining constant
concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov
(master-equation) description of a motor protein, we illustrate that the NESS
and QSS have identical kinetics as well as the Second Law in terms of a same
positive entropy production rate. The difference between the heat dissipation
of a NESS and its corresponding QSS is exactly the $W_{min}$. This provides a
justification for introducing an {\em ideal external regenerating system} and
yields 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 of
chemical 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 in
stochastic thermodynamics, and identify a relative entropy $H$ as a generalized
free energy.
