Quantum analysis and nonequilibrium response

Abstract

The quantum derivatives of e-A, A-1 and log A, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator A in a Hilbert space. Using the quantum analysis based on these quantum derivatives, a basic equation for the entropy operator in nonequilibrium systems is derived, and Zubarev's theory is extended to infinite order with respect to a perturbation. Using the first-order term of this general perturbational expansion of the entropy operator, Kubo's linear response is rederived and expressed in terms of the inner derivation δH for the relevant Hamiltonian H. Some remarks on the conductivity σ(w) are given.