  We show that in four-dimensional gauge theories dual to five-dimensional
Einstein gravity coupled to a single scalar field in the bulk the derivative of
the single heavy quark free energy in the deconfined phase is $dF_{Q}(T)/dT
\sim -1/c_s^2(T)$, where $c_s(T)$ is the speed of sound. This general result
provides a direct link between the softest point in the equation of state of
strongly-coupled plasmas and the deconfinement phase transition described by
the expectation value of the Polyakov loop. We give an explicit example of a
gravity dual with black hole solutions that can reproduce the lattice results
for the expectation value of the Polyakov loop and the thermodynamics of SU(3)
Yang-Mills theory in the (non-perturbative) temperature range between $T_c$ and
$3T_c$.
