  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.
