 Magnetic entropy

Magnetic entropy counts the uncertainty in the occupied magnetic microstates. For independent localized magnetic moments with one-site probabilities $p_j$,where $N$ counts sites and $k_B$ is the Boltzmann constant. This is the Gibbs entropy for the magnetic degrees of freedom. Equal occupation of two states gives $N{k}_B\ln 2$; certain occupation of one state gives zero. Calling this disorder is useful only if the relevant states and their probabilities are specified. In an interacting material, correlations generally prevent replacing the many-body Gibbs entropy by this sum of independent one-site contributions.

Increasing the magnetic field at fixed positive temperature favors lower magnetic energy levels, reducing magnetic entropy. During ideal isolated demagnetization, both the level separation and temperature fall together, leaving the occupation probabilities unchanged. Thus the independent-spin idealization cools without increasing spin disorder along the isolated leg. When a real crystal's vibrating lattice also cools, its lost entropy can instead be taken up by the magnetic degrees of freedom. The conserved quantity is the total entropy of the thermally isolated stage, including any attached load in thermal equilibrium.