Linear response theory for nonequilibrium stationary systems

A nonequilibrium statistical mechanics is developed by extending the Kubo-Nakano theory of linear response to spatially inhomogeneous systems under the action of external fields. It is argued that the standard linear response theory bases upon the fluctuation-dissipation theorem. The stationary density matrix of the nonequilibrium system is given by applying Zubarevʹs method. It is found that Onsagerʹs reciprocity relations require a redefinition of the responses to external fields, reflecting the fact that the stationary density matrix is not of the standard canonical form with the unperturbed Hamiltonian. Following Nakano, a variational principle is developed for nonequilibrium stationary systems. A link of the variational principle with Machlup-Onsager theory is explored.