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We find analytic asymptotic expressions at low temperature for the Casimirfree energy, entropy and pressure of two parallel graphene sheets in theframework of the Lifshitz theory. The reflection coefficients ofelectromagnetic waves on graphene are described on the basis of firstprinciples of quantum electrodynamics at nonzero temperature using thepolarization tensor in (2+1)-dimensional space-time. The leading contributionsto the Casimir entropy and to the thermal corrections to the Casimir energy andpressure are given by the thermal correction to the polarization tensor atnonzero Matsubara frequencies. It is shown that the Casimir entropy for twographene sheets goes to zero when the temperature vanishes, i.e., the third lawof thermodynamics (the Nernst heat theorem) is satisfied. At low temperature,the magnitude of the thermal correction to the Casimir pressure between twographene sheets is shown to vary inversely proportional to the separation. TheNernst heat theorem for graphene is discussed in the context of problemsoccurring in Casimir physics for both metallic and dielectric plates.

Nernst heat theorem for the thermal Casimir interaction between two graphene sheets