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 ${\delta }_{\mathcal{H}}$ for the relevant Hamiltonian $\mathcal{H}$. Some remarks on the conductivity $\sigma (\omega )$ are given.

Latex, 16 pages, no figures, to be published in Prog. Theor. Phys. (1998)

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