  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.
