Possible non-additive entropy based on the alpha-deformed addition

Abstract

We reexamine the non-additive entropy which was first proposed by Tsallis [1] where this deformed entropy (q-entropy) is related to a special map. We consider a new map giving the alpha-additive property. Based on this, we propose a new type of non-additive entropy which we call alpha-entropy and derive the alpha-deformed Boltzmann factor and alpha-deformed free energy. As an example, we discuss the black body radiation in the alpha-deformed thermodynamics where we regard photon as a particle obeying alpha-deformed boson algebra.