q-Deformed structures and generalized thermodynamics

On the basis of the recently proposed formalism 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.