Some implications of three generalized uncertainty principles in statistical mechanics of an ideal gas

Several approaches to quantum gravity and high-energy physics predict the existence of a minimum length scale due to quantum gravitational corrections leading to the deformation/generalization of the uncertainty principle (GUP). Various mathematical forms of GUP were introduced in the literature and their implications in different fields ranging from nanoscale to large scale were discussed in the literature. In this paper, we study three dissimilar forms of GUP and we discuss their implications in statistical mechanics of an ideal gas. A number of features were obtained, discussed, and analyzed accordingly.