  The statistical proprieties of complex systems can differ deeply for those of
classical systems governed by Boltzmann-Gibbs entropy. In particular, the
probability distribution function observed in several complex systems shows a
power law behavior in the tail which disagrees with the standard exponential
behavior showed by Gibbs distribution. Recently, a two-parameter deformed
family of entropies, previously introduced by Sharma, Taneja and Mittal (STM),
has been reconsidered in the statistical mechanics framework. Any entropy
belonging to this family admits a probability distribution function with an
asymptotic power law behavior. In the present work we investigate the Legendre
structure of the thermostatistics theory based on this family of entropies. We
introduce some generalized thermodynamical potentials, study their
relationships with the entropy and discuss their main proprieties.
Specialization of the results to some one-parameter entropies belonging to the
STM family are presented.
