Abstract We investigate the thermostatistics of relativistic ideal gases within the recently proposed deformed Heisenberg algebra (Perivolaropoulos, 2017), which includes a maximal length. By using the semiclassical method, the generalized canonical partition function is established and the modified thermodynamic functions are then calculated. It is explicitly shown that the maximal length, unlike the minimal length, modifies the equation of state of relativistic ideal gases. Furthermore, the ultrarelativistic and nonrelativistic regimes are discussed. In contrast to the minimal length corrections, the maximal length corrections do not depend on the considered regime. Such a result confirms that the effects of the maximal length and those of the minimal length are fundamentally different.

中文翻译：

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关于存在最大长度的相对论理想气体的热力学

摘要 我们在最近提出的变形海森堡代数 (Perivolaropoulos, 2017) 中研究了相对论理想气体的热力学，其中包括最大长度。采用半经典方法建立广义正则配分函数，计算修正后的热力学函数。明确地表明，与最小长度不同，最大长度修改了相对论理想气体的状态方程。此外，还讨论了超相对论和非相对论制度。与最小长度修正相反，最大长度修正不取决于所考虑的制度。这样的结果证实了最大长度和最小长度的影响是根本不同的。