论文标题
最大长度变形空间的恒温术
Thermostatistics in deformed space with maximal length
论文作者
论文摘要
由Fityo开发的变形的海森堡代数（Fityo，2008年）计算的规范分区函数的方法适用于修改后的换向关系，包括最大长度，该长度最近由Perivolaropoulos（Perivolaropoulos，Perivolaropoulos，2017）在1D中提出。首先，最大长度变形代数的形式主义扩展到任意维度。然后，通过采用适应的半经典方法，研究了理想气体和谐波振荡器系统（HOS）的恒温量。对于理想的气体，结果概括了我们最近在1D中获得的结果（Bensalem and Bouaziz，2019年），并在半经典和量子方法之间显示出完全一致的一致性。特别是，在3D中建立了理想气体的较硬的现实状态方程。这与我们在上述论文中提出的正式形式一致。通过分析一些实验数据，我们认为最大长度可能被视为与正在研究的系统相关的宏观尺度。最后，与理想气体相比，HOS系统的恒温量表明，最大长度的影响取决于研究的系统。另一方面，观察到，最大长度对HOS的热力学功能的最大效应类似于文献中先前研究的最小长度。
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.
