Entropy and Heat Capacity of a Degenerate Neutron Gas in a Magnetic Field

Abstract

General expressions for the dependence of the entropy of a degenerate neutron gas in a magnetic field on the magnetic field magnitude and the neutron concentration with allowance for the anomalous magnetic moment (AMM) of the neutrons have been obtained in implicit form, and the dependence of the so-called reduced entropy on the field is represented in graphical form for the neutron concentration C = 1038 cm–3, which is typical of neutron stars. Analytical estimates have been made for a field magnitude of ~1019 G, which is possible in neutron stars, and this neutron concentration ~ 1038 cm–3 including when the neutron gas is close to its saturation state with preferred orientation of the AMM of the neutrons in the direction of the field. It is shown that the entropy decreases with increasing field as the neutron gas approaches its saturation state, when the AMM of all the neutrons is oriented in the direction of the field. This is consistent with the second law of thermodynamics, so that the evolution of neutron stars (magnetars), accompanied by an increase in the field, is therefore unlikely, regardless of the reasons for the appearance of the magnetic field. The heat capacity of the degenerate neutron gas is also found, and turns out to be formally equal to the entropy in the absence of a magnetic field.