▎ 摘　　要

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap Delta and chemical potential mu are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2 + 1)-dimensional space-time. Different asymptotic expressions arc found under the conditions Delta > 2 mu, Delta = 2 mu, and Delta < 2 mu taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both Delta > 2 mu and Delta < 2 mu the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for Delta = 2 mu this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.