Postulating the smoothness of the phase space distribution function, a
s done by Tuckerman ct al. [Phys. Rev. Lett. 78 (1997) 2042], we show
that the phase space density is conserved when a proper smooth geometr
ical factor (the Jacobian) can be defined and is correctly taken into
account. As a result, many thermodynamic concepts can be carried over
to characterize the non-equilibrium steady state. (C) 1998 Elsevier Sc
ience B.V.