The fluctuation-dissipation theorem in the framework of the Tsallis statistics

Abstract

In the framework of a generalized statistical mechanics introduced recently by Tsallis (1993), we derive a generalized form of the fluctuation-dissipation theorem, which expresses a relation between extended susceptibilities and equilibrium fluctuations. To achieve this, we consistently propose a generalized functional form For the instantaneous distribution function. The present theorem recovers as particular cases the corresponding generalized relations already obtained for the specific heat in terms of the generalized energy fluctuations and for the susceptibility of a magnetic system under the action of a uniform magnetic field.