Canonical partition function for anomalous systems described by the kappa-entropy

Starting from the K-distribution function, obtained by applying the maximal entropy principle to the kappa-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical kappa-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the kappa-partition function. The relationship between the associated kappa-free energy and the kappa-entropy is also discussed.