  We study the ratio of the entropy to the total energy in conformal field
theories at finite temperature. For the free field realizations of N=4 super
Yang-Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is
bounded from above. The corresponding bounds are less stringent than the
recently proposed Verlinde bound. For strongly coupled CFTs with AdS duals, we
show that the ratio obeys the Verlinde bound even in the presence of rotation.
For such CFTs, we point out an intriguing resemblance in their thermodynamic
formulas with the corresponding ones of two-dimensional CFTs. The discussion is
based on hep-th/0101076.
