Entropy and heat capacity of degenerated neutron gas in a magnetic field

This article is devoted to obtaining general expressions for the dependence of the entropy of a degenerate neutron gas in a magnetic field, taking into account the anomalous magnetic moment (AMM) of neutrons on the magnetic field and the neutron concentration. Also an attempt was made in graphical form to represent the dependence of the so-called “reduced entropy” on the magnetic field induction at a concentration of neutrons C = 10³⁸ cм^-3 typical of neutron stars. Analytical estimates were made for the possible magnitude of the field ~ 10¹⁹ G in the neutron stars and the same concentration of neutrons, including the case when the neutron gas is close to the saturation state with the preferred orientation of the AMM of all neutrons in the direction of the field. It is shown that entropy decreases with increasing field as the neutron gas approaches the saturation state, when the AMM of all neutrons is oriented along the field. It was also stated that 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 a magnetic field. The heat capacity of the degenerate neutron gas was also determined, which turned out to be formally equal to the entropy, as is the case in the absence of a magnetic field.

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