Canonical thermostatics of the ideal gas in the framework of the generalized uncertainty principle

In this study, The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the socalled Generalized Uncertainty Principle (GUP) of the second order. In the framework of the considered GUP scenario, a unique partition function is obtained by using two different methods of quantum and classical approaches. It should be noticed that here we consider the magnitude of the momentum in the deformed Hamiltonian of the model. In this way, the model is different from the already existing model which does not have any significant result in the quantum approach. In particular, the corrections to the thermodynamical characteristics such as the mean energy, the entropy and the density of states are achieved. The induced improvements manifest themselves at very high-temperature limits. However, it is shown that, if one applies the predicted observational bound on the GUP deformation parameter, the modifications become more observable even at intermediate temperatures. The deformation parameter of the considered GUP model is also estimated for nowadays precision of measurements of the heat capacity of an ensemble of hydrogen atoms.