Canonical ensemble in non-extensive statistical mechanics, q>1q>1

•Reservoir having large generalized heat capacity leads to the Tsallis statistics.•Short-range interactions with such a reservoir lead to qq-exponential factor.•Generalized heat capacity with q>1q>1 leads to a negative physical heat capacity.•The condition of applicability of canonical ensemble is the same for all values of qq.

The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily lead to physical insight. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics by considering a small system interacting with a large reservoir via short-range forces and assuming equal probabilities for all available microstates. We concentrate on the situation when the reservoir is characterized by generalized entropy with non-extensivity parameter q>1q>1. We also investigate the problem of divergence in the non-extensive statistical mechanics occurring when q>1q>1 and show that there is a limit on the growth of the number of microstates of the system that is given by the same expression for all values of qq.