  We discuss general spinning p-branes of string and M-theory and use their
thermodynamics along with the correspondence between near-horizon brane
solutions and field theories with 16 supercharges to describe the thermodynamic
behavior of these theories in the presence of voltages under the R-symmetry.
The thermodynamics is used to provide two pieces of evidence in favor of a
smooth interpolation function between the free energy at weak and strong
coupling of the field theory. (i) A computation of the boundaries of stability
shows that for the D2, D3, D4, M2 and M5-branes the critical values of Omega/T
in the two limits are remarkably close and (ii) The tree-level R^4 corrections
to the spinning D3-brane generate a decrease in the free energy at strong
coupling towards the weak coupling result. We also comment on the
generalization to spinning brane bound states and their thermodynamics, which
are relevant for non-commutative field theories.
