Dissipation coefficients and conductances in mesoscopic systems without time reversal invariance

It is shown that in the presence of a magnetic field a multi-probe generalization of the Landauer formula can be derived from linear response theory. The symmetric and antisymmetric parts of the current with respect to magnetic field reversal are discussed separately to show that the symmetrized conductances obtained by Stone and Szafer for zero magnetic field are the coefficients in the quadratic form which relates the asymptotic values of the potential to the power dissipated outside the mesoscopic sample. A derivation of the reciprocity theorem is given without using Büttiker's version of the Landauer formula.