  On the basis of the recently proposed formalism [A. Lavagno and P.N. Swamy,
Phys. Rev. E 65, 036101 (2002)], we show that the realization of the
thermostatistics of q-deformed algebra can be built on the formalism of
q-calculus. It is found that the entire structure of thermodynamics is
preserved if we use an appropriate Jackson derivative instead of the ordinary
thermodynamic derivative. Furthermore, in analogy with the quantum q-oscillator
algebra, we also investigate a possible q-deformation of the classical Poisson
bracket in order to extend a generalized q-deformed dynamics in the classical
regime.
