  Consider a small sample coupled to a finite number of leads, and assume that
the total (continuous) system is at thermal equilibrium in the remote past. We
construct a non-equilibrium steady state (NESS) by adiabatically turning on an
electrical bias between the leads. The main mathematical challenge is to show
that certain adiabatic wave operators exist, and to identify their strong limit
when the adiabatic parameter tends to zero. Our NESS is different from, though
closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle
approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971
regarding the (non)equivalence between the partitioned and partition-free
approaches.
