Magnetic entropy deficit ($\Delta s_{\mathrm{mag}}=s_{\max }-s(T,B)$)

The magnetic entropy deficit is the entropy increase still available to independent moments as their field polarization is removed. For a spin-$J$ multiplet, $s_{\max }=k_B\ln (2J+1)$ and the high-temperature deficit is $k_{B}J(J+1)[g{\mu }_{B}B/(k_{B}T){]}^2/6$. Isothermal magnetization creates this deficit while rejecting heat to a bath. Subsequent reversible demagnetization can absorb entropy from a cooling load. The deficit, not the initial absolute magnetic entropy, measures that capacity.