Thermal expansion coefficient and isothermal and adiabatic compressibilities of the relativistic free electron gas

We investigate the thermodynamic response of an ideal relativistic electron gas by calculating its thermal expansion coefficient as well as its isothermal and adiabatic compressibilities at finite temperature. Analytical results are obtained in the non-relativistic and ultra-relativistic limits, highlighting the transition between the classical and strongly relativistic regimes, i.e., a transition relevant to compact astrophysical objects. In the zero-temperature degeneracy limit, our expressions underscore the dominant role of Fermi pressure in determining the stiffness of the equation of state, a key factor for modeling white dwarfs and neutron star crusts. These results thus provide useful data for developing astrophysical equations of state in dense plasmas.