  In this paper we introduce a method of calculating the local temperature and
chemical potential inside a mesoscopic device out of equilibrium. We show how
to check the conditions of local thermal equilibrium as the whole system is out
of equilibrium. Especially we study the onsite chemical potentials inside a
chain coupled to two reservoirs at a finite voltage bias. In the presence of
disorder we observe a large fluctuation in onsite chemical potentials, which
can be suppressed by the electron-electron interaction. By taking average with
respect to the configurations of disorder, we recover the classical picture
where the voltage drops monotonously through the resistance wire. We prove the
existence of local intensive variables in a mesoscopic device which is in
equilibrium or not far from equilibrium.
