  Nonextensive statistics is a formalism of statistical mechanics that
describes the ocurrence of power-law distributions in complex systems,
particularly the so-called $q$ exponential family of distributions. In this
work we present the use of fluctuation theorems for $q$-canonical ensembles as
a powerful tool to readily obtain statistical properties. In particular, we
have obtained strong conditions for the possible values of $q$ depending on the
density of states of the system.
