Pauli paramagnetic gas in the framework of Riemannian geometry

We investigate the thermodynamic curvature resulting from a Riemannian geometry approach to thermodynamics for the Pauli paramagnetic gas which is a system of identical fermions each with spin 1 / 2, and also for classical ideal paramagnetic gas. We find that both the curvature of classical ideal paramagnetic gas and the curvature of the Pauli gas in the classical limit reduce to that of a two-component ideal gas. On the other hand, it is seen straightforwardly that the curvature of classical gas satisfies the geometrical equation exactly. Also a simple relationship between the curvature of Pauli gas and the correlation volume is obtained. We see that it is only in the classical and semiclassical regime that the absolute value of the thermodynamic curvature can be interpreted as a measure of the stability of the system.