Thermostatistics in deformed space with maximal length

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 maximal length, proposed in 1D by Perivolaropoulos (Perivolaropoulos, 2017). Firstly, the one-dimensional maximum length formalism 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. The modified 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 effects on some thermodynamic functions of the HOs are analogous to those of the minimal length, studied previously in the literature. Finally, by analyzing some experimental data, we argue that the maximal length might be viewed as a characteristic scale associated with the system under study.