Quantum Oscillators: Applications in Statistical Mechanics

We consider a canonical ensemble of q oscillators. Using classical realization for q oscillator algebra, 17 we calculate, for a small real q, the partition function and thermodynamic potentials F, E and S. We show that F reaches the minimum and E and S the maximum (as functions of the deformation parameter q) when q = 1 (for the classical oscillator). We argue about possible far-reaching consequences of this fact. As an application we obtain a first quantum correction to Planck's black body radiation law. We introduce the slightly deformed oscillator (SDO) model, which provides us with a significant amount of information about the system. When q = 1, our results are shown to coincide with classical results.