Statistical description of an ideal gas in maximum length quantum mechanics

Abstract

We discuss the effects of the recent proposed Generalized Uncertainty Principle (GUP) (Perivolaropoulos, 2017), which includes a maximum length on the thermostatistics of an ideal gas. In the framework of this modified version of quantum mechanics, the deformed Schrödinger equation is solved analytically for a particle in an infinite square-well potential, then the corresponding energy spectrum is extracted. By computing the modified canonical partition function, the thermodynamic properties of the system are investigated within the canonical and microcanonical ensembles; the results show a complete consistency between both statistical descriptions. Furthermore, a comparison with the results obtained in the context of the minimal length GUP indicates that the maximum length induces fundamentally different effects, which become important at high temperatures and for large space confining the system. Especially, a modified equation of state, similar to that of real gases, emerges in the scope of this new formalism.