Effect of a magnetic field on the transport coefficients of a system of electrons

Abstract

Kohler's variational principle is shown to lead rigorously to the conclusion that for fixed thermodynamic forces the entropy production is always decreased by the application of a magnetic field. This implies that the transport coefficients (including those describing thermal transport) obey certain inequalities. In particular we find that within the framework of the semi-classical Boltzmann equation the result, that on the application of a magnetic field the resistance must always increase, is an exact finding.