Effect of the Minimal Length on the Thermodynamics of Ultra-Relativistic Ideal Fermi Gas

Based on the generalized uncertainty principle, the thermodynamics of Fermi gas in high density, high pressure and high temperature are calculated. As the temperature and density increases, the energy and entropy becomes saturated and the pressure blows up without any bound. Using the conservation equation of the Robertson–Walker cosmology, we find that, when the energy exceeds the E_H=β₀^?1/2c²M_p, the expansion cannot be driven by the photon gas and the fermion gas. This requires some new physical mechanism related to quantum gravity, such as tachyons and dilatons.