  By working with the free energy for the type II supergravity near-horizon
solution of N coincident non-extremal Dp-branes we study the transitions among
the non-conformal Dp-brane system, the perturbative super Yang-Mills theory and
a certain system associated with M theory. We derive a relation between this
free energy and the action of a Dp-brane probe in the N Dp-brane background.
Constructing the free energy for the five dimensional black hole labeled by the
D1-brane and D5-brane charges we find the similar relation between it and the
action of a D1 or D5 brane probe in the D1 + D5 brane background. These
relations are explained by the massive open strings stretched between the
relevant D-branes
