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Two different interpretations of q-boson algebra and a new q-deformed statistical physics

In this paper we consider q-boson algebra from two different types of q-derivatives (Jackson’s q-derivative and Tsallis’ q-derivative). We used the q-deformation of Newton’s instantaneous rate of change to obtain the Tsallis’ q-derivative. Using this we investigate the algebraic structure of q-boson algebra. We discuss the canonical ensemble for the q-boson and compute some thermodynamic quantities.