We discuss how the Lagrange multiplier method of nonequilibrium steady state statistical mechanics can be applied to describe the electronic transport in a quantum wire. We describe the theoretical scheme using a tight-binding model. The Hamiltonian of the wire is extended via a Lagrange multiplier to "open" the quantum system and to drive current through it. The diagonalization of the extended Hamiltonian yields the transport properties of wire. We show that the Lagrange multiplier method is equivalent to the Landauer approach within the considered model. (C) 2004 American Institute of Physics.