Abstract. We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e., the Nernst theorem is violated. The experimental situation is also discussed.

We derive perturbation analytic expressions for the Casimir free energy and entropy between two dissimilar ferromagnetic plates which are applicable at arbitrarily low temperature. The dielectric properties of metals are described using either the nondissipative plasma model or the Drude model taking into account the dissipation of free charge carriers. Both cases of constant and frequency-dependent magnetic permeability are considered. It is shown that for ferromagnetic metals described by the plasma model the Casimir entropy goes to zero when the temperature vanishes, i.e., the Nernst heat theorem is satisfied. For ferromagnetic metals with perfect crystal lattices described by the Drude model the Casimir entropy goes to a nonzero constant depending on the parameters of a system with vanishing temperature, i.e., the Nernst heat theorem is violated. This constant can be positive which is quite different from the earlier investigated case of two nonmagnetic metals.

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