Abstract
A dynamic theory of the linear reaction from nonextensive quasi-equilibrium multibody systems to an external time-dependent perturbation is developed in quantum statistical mechanics based on the Tsallis parametric nonadditive entropy associated with the density matrix. For nonextensive quantum systems, a modification of the Kubo theory developed in quantum mechanics is proposed. The linear reaction theory is constructed based on a generalized canonical form of the density matrix obtained by maximizing the Tsallis quantum entropy by averaging the observed values over the escort distribution. Generalized expressions for admittance and response functions are presented that describe the linear response of the system to a weak external mechanical impact. The paper discusses the symmetry property for the relaxation function under time reversal and the Onsager reciprocity relation for generalized susceptibility. It is shown that these properties known in classical quantum statistics remain valid for anomalous systems.
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