Thermostatistical properties of the blackbody radiation and Debye crystal model through Fibonacci oscillators

Abstract

In this study, we consider a deformed gas of the bosonic Fibonacci oscillators, whose properties enable us to develop both an intermediate-statistics behavior and an energy spectrum given by a generalized Fibonacci sequence in terms of the real independent deformation parameters q(1) and q(2). By viewing photons and phonons as the particles obeying the commuting Fibonacci oscillator algebra, we extensively discuss several thermodynamical and statistical properties of the blackbody radiation and Debye crystal model. We then investigate possible roles of the deformation parameters q(1) and q(2) on the thermostatistics of such deformed photon and deformed phonon gases. Finally, we compare our results with the results of both the non-extensive Tsallis statistics and the usual (undeformed) Bose gas case. The approach presented here could give new insights for further studies of deformed quantum thermodynamics and its potential applications such as in understanding the properties of early universe as well as modeling a possible candidate of dark matter.