Dynamic Linear Response Theory for a Nonextensive System Based on the Tsallis Prescription

We develop here a dynamic linear response theory of many-body nonextensive systems based on the maximization of the Tsallis entropy associated with the density matrix and the concomitant suitably defined mean total energy, number, etc., where the averaging is over the qth power of the density matrix, q being a parameter characterizing the nonextensivity. This formulation is shown to preserve causality (Kramers-Kronig), time reversal, and Onsager reciprocity, while a different form of fluctuation-dissipation theorem is obtained. The traditional theory for extensive systems is obtained in the special case where $q=1\mathrm{}$.