On the use of non-canonical quantum statistics

We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more understanding on the standard Boltzmann-Gibbs statistics and on the recently developed Tsallis statistics. We conclude on a discussion of the role of entropy and the maximum entropy principle in thermodynamics.