GUP with minimal length and maximal momentum on the thermodynamics of relativistic fermi gas

This work attempts to investigate the influence of the linear and quadratic generalized uncertainty principle (LQGUP) on the thermodynamical characteristics of relativistic Fermi gas. The general thermodynamical characteristics of relativistic Fermi gas, such as mean energy, pressure, entropy, and specific heat, are obtained. According to the modified function of temperature for mean energy and specific heat of relativistic Fermi gas, we find that at high temperature limit, the value of deformation parameter in the framework of LQGUP has an important effect on thermodynamic characteristics. It appears that the deformation parameter’s value is rising at higher energy levels of science, resulting in the minimal measurable length reaching close to the Planck length scale.