Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and other considers extension of concept entropy, i.e., Tsallis statistics. reviewed discussed some main properties these approaches thermal Green function formalism perform developments, simultaneously allowing us analyze each case’s dynamics thermodynamics aspects. In particular, results allow understand how extensions change behavior quantities, particularly fluctuations related system.