A degenerate Fermi gas is a state of matter formed by fermions, which are particles that follow the Pauli exclusion principle. In this state, the particles occupy the lowest available energy levels at absolute zero temperature, leading to a high density of particles. This results in unique quantum behaviors, as the particles cannot be in the same quantum state. In a degenerate Fermi gas, the pressure and temperature are not directly related as in classical gases. Instead, the properties are determined by the Fermi energy, which is the energy of the highest occupied state at absolute zero. This phenomenon is significant in fields like condensed matter physics and astrophysics, particularly in understanding white dwarfs and neutron stars.