Thermostatistics in deformed space with maximal length

TL;DR

This paper extends the thermostatistical analysis of deformed Heisenberg algebra with a maximal length to higher dimensions, examining ideal gases and harmonic oscillators, and discusses potential experimental implications of the maximal length scale.

Contribution

It develops a multidimensional formalism for maximum length deformed algebra and analyzes its effects on thermodynamics of ideal gases and harmonic oscillators.

Findings

Complete agreement between semiclassical and quantum results for ideal gases.

Maximal length leads to a stiffer equation of state in 3D.

Effects of maximal length vary between different systems, similar to minimal length effects.

Abstract

The method for calculating the canonical partition function with deformed Heisenberg algebra, developed by Fityo (Fityo, 2008), is adapted to the modified commutation relations including a maximum length, proposed recently in 1D by Perivolaropoulos (Perivolaropoulos, 2017). Firstly, the formalism of 1D maximum length deformed algebra is extended to arbitrary dimensions. Then, by employing the adapted semiclassical approach, the thermostatistics of an ideal gas and a system of harmonic oscillators (HOs) is investigated. For the ideal gas, the results generalize those obtained recently by us in 1D (Bensalem and Bouaziz, 2019), and show a complete agreement between the semiclassical and quantum approaches. In particular, a stiffer real-like equation of state for the ideal gas is established in 3D; it is consistent with the formal one, which we presented in the aforementioned paper. By analyzing some experimental data, we argue that the maximal length might be viewed as a macroscopic scale associated with the system under study. Finally, the thermostatistics of a system of HOs compared to that of an ideal gas reveals that the effects of the maximal length depend on the studied system. On the other hand, it is observed that the maximal length effect on some thermodynamic functions of the HOs is analogous to that of the minimal length, studied previously in the literature.