  A classical particle system coupled with a thermostat driven by an external
constant force reaches its steady state when the ensemble-averaged drift
velocity does not vary with time. The statistical mechanics of such a system is
derived merely based on the equal probability and ergodicity principles, free
from any conclusions drawn on equilibrium statistical mechanics or local
equilibrium hypothesis. The momentum space distribution is determined by a
random walk argument, and the position space distribution is determined by
employing the equal probability and ergodicity principles. The expressions for
energy, entropy, free energy, and pressures are then deduced, and the relation
among external force, drift velocity, and temperature is also established.
Moreover, the relaxation towards its equilibrium is found to be an
exponentially decaying process obeying the minimum entropy production theorem.
