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We show that the density matrix for a finite conductor attached to reservoirsobtained by Keldysh formalism is of MacLennan-Zubarev form. On the basis of thefact that the density matrix is the invariant part proposed by Zubarev, it isshown that Keldysh formalism may describe the irreversible processes andsteady-state feature of the system. An important consequence of theMacLennan-Zubarev form of the density matrix is a generalization of the Kuboformula in a nonequilibrium case. On the basis of the result, we propose theformula of shot noise and a nonequilibrium identity between differentialconductance, noise power and shot noise as a generalized Nyquist-Johnsonrelation.

Nonequilibrium Kubo Formula of Finite Conductor Connected to Reservoirs based on Keldysh Formalism