Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary

In the present paper we investigate thermal fluctuation corrections to vacuum energy at zero temperature of a conformally coupled massless scalar field whose modes propagate in Einstein universe with spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, generalize results found literature this scenario, which has considered only temperature. To do this, use generalized zeta function method plus Abel-Plana formula calculate renormalized Casimir free as well other thermodynamics quantities, namely, internal entropy. For each one them also limits high low temperatures. At temperatures that presents classical contributions, along logarithmic term. Also limit, contribution entropy term addition well. Conversely, temperatures, it is shown are dominated It obeys third law thermodynamics.