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The method for calculating the canonical partition function with deformedHeisenberg algebra, developed by Fityo (Fityo, 2008), is adapted to themodified commutation relations including a maximum length, proposed recently in1D by Perivolaropoulos (Perivolaropoulos, 2017). Firstly, the formalism of 1Dmaximum length deformed algebra is extended to arbitrary dimensions. Then, byemploying the adapted semiclassical approach, the thermostatistics of an idealgas and a system of harmonic oscillators (HOs) is investigated. For the idealgas, the results generalize those obtained recently by us in 1D (Bensalem andBouaziz, 2019), and show a complete agreement between the semiclassical andquantum approaches. In particular, a stiffer real-like equation of state forthe ideal gas is established in 3D; it is consistent with the formal one, whichwe presented in the aforementioned paper. By analyzing some experimental data,we argue that the maximal length might be viewed as a macroscopic scaleassociated with the system under study. Finally, the thermostatistics of asystem of HOs compared to that of an ideal gas reveals that the effects of themaximal length depend on the studied system. On the other hand, it is observedthat the maximal length effect on some thermodynamic functions of the HOs isanalogous to that of the minimal length, studied previously in the literature.

Thermostatistics in deformed space with maximal length