Formula of shot noise in a mesoscopic conductor based on Keldysh formalism

On the basis of Keldysh formalism we clarify that the density matrix of a mesoscopic conductor is one of the MacLennan–Zubarev ensembles. As a consequence the differential conductance is expressed as sum of two types of correlation functions, which we call a nonequilibrium Kubo formula. We propose that one of them is the formula of shot noise; the other is well known as noise power. We derive an extended Nyquist–Johnson relation in correlated systems between differential conductance, noise power and shot noise.