Thermostatistics of a q-deformed boson gas

We show that a natural realization of the thermostatistics of q bosons can be built on the formalism of q calculus, and that the entire structure of t hermodynamics is preserved if we use an appropriate Jackson derivative in p lace of the ordinary thermodynamics derivative. This framework allows us to obtain a generalized q boson entropy which depends on the q basic number. We study the ideal ri boson gas in the thermodynamic limit which is shown t o exhibit Bose-Einstein condensation with a higher critical temperature and a discontinuous specific heat.