# Relation between external magnetic field intensity H, magnetisation M and the entropy?

How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in terms of M.

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Per Kittel's "Elementary Statistical Physics":

$$dQ=dU_A+MdH$$.

Where $dU_A$ does not include the magnetic field energy as part of the system.

An alternative, equivalent, formulation is

$$dQ=dU_B-HdM$$

Where $dU_B$ does include the field energy: $U_A=U_B-\mathbf{H \cdot M}$.

With $dQ=TdS$, I think you're there...

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