Based on the spin fluctuation mechanism we have succeeded in deriving formulae for
the magnetic entropy and the specific heat of itinerant electron ferromagnets
that cover the wide range of the temperature and the external field strength.
We show that it is necessary to include an extra term into the free energy for a
thermodynamically consistent treatment. We are able to predict several new features on the
temperature and the external field dependence, an extra enhancement of the
T-linear coefficient at low temperature and the presence of a critical peak anomaly of the
specific heat, for instance. They result from terms proportional to the second-order
temperature derivative of the spontaneous magnetization. The presence of the terms is
connected with the Maxwell relation of thermodynamics.