Equation of state of the free electron gas in a magnetic field at arbitrary degeneracy

We study the equation of state of the non-relativistic free-electron gas in a constant magnetic field at arbitrary degeneracy based on the seminal work of Biswas et al. [Phys. Plasmas 20, 052503 (2013)]. The approach naturally unifies the Pauli paramagnetism, the Landau diamagnetism, and the de Haas–van Alphen effect. We consider the magnetization and the susceptibility as well as various thermodynamic quantities. In particular, the specific heats at constant volume and constant pressure are calculated, from which the adiabatic index is obtained. Weak and strong field limits are examined in detail. It is shown that the various quantities of interest saturate at strong magnetic field. Results are consistent with previous calculations performed at zero magnetic field. The polylogarithms are more adapted than the Fermi–Dirac integrals to describe the present system. The de Haas–van Alphen effect is not restricted to the magnetization and susceptibility but can be seen for other thermodynamic quantities.