In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around generalization of Heisenberg uncertainty principle. This misconception stems from series recently published works in which perturbative and non-perturbative methods are confused, thereby resulting blurring distinction between changes deformed algebra representation opera...

The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the so-called Generalized Uncertainty Principle (GUP) of the second order. In the frame work of the considered GUP scenario, a unique partition function is obtained by using of two different methods of quantum and classical approaches. It should be noti...