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We calculate the high temperature partition functions for SU(Nc) or U(Nc)gauge theories in the deconfined phase on S^1 x S^3, with scalars, vectors,and/or fermions in an arbitrary representation, at zero 't Hooft coupling andlarge Nc, using analytical methods. We compare these with numerical resultswhich are also valid in the low temperature limit and show that the Bekensteinentropy bound resulting from the partition functions for theories with anyamount of massless scalar, fermionic, and/or vector matter is always satisfiedwhen the zero-point contribution is included, while the theory is sufficientlyfar from a phase transition. We further consider the effect of adding massivescalar or fermionic matter and show that the Bekenstein bound is satisfied whenthe Casimir energy is regularized under the constraint that it vanishes in thelarge mass limit. These calculations can be generalized straightforwardly forthe case of a different number of spatial dimensions.

Bekenstein entropy bound for weakly-coupled field theories on a 3-sphere