Thermodynamics of Neutrons in a Magnetic Field and its Implications for Neutron Stars

We investigate the effects of a magnetic field on the thermodynamics of a neutron system at finite density and temperature. Our main motivation is to deepen the understanding of the physics of a class of neutron stars known as magnetars, which exhibit extremely strong magnetic fields. Taking into account two facts, (i) the existence of a pressure anisotropy in the presence of a magnetic field and (ii) that the quantum field theory contribution to the pressure is non-negligible, we show that the maximum value that the inner magnetic field of a star can reach while being in agreement with the magnetohydrostatic equilibrium between the gravitational and matter pressures becomes $10^{17}$ G, an order of magnitude smaller than the previous value obtained through the scalar virial theorem; that the magnetic field has a negligible effect on the neutron system's equation of state; that the system's magnetic susceptibility increases with the temperature; and that the specific heat $C_V$ does not significantly change with the magnetic field in the range of temperatures characteristic of protoneutron stars.