  We consider the classical and local thermodynamic stability of non- and
near-extremal Dp-branes smeared on a transverse direction. These two types of
stability are connected through the correlated stability conjecture for which
we give a proof in this specific class of branes. The proof is analogous to
that of Reall for unsmeared branes, and includes the construction of an
appropriate two-parameter off-shell family of smeared Dp-brane backgrounds. We
use the boost/U-duality map from neutral black strings to smeared black branes
to explicitly demonstrate that non-and near-extremal smeared branes are
classically unstable, confirming the validity of the conjecture. For
near-extremal smeared branes in particular, we show that a natural definition
of the grand canonical ensemble exists in which these branes are
thermodynamically unstable, in accord with the conjecture. Moreover, we examine
the connection between the unstable Gregory-Laflamme mode of charged branes and
the marginal modes of extremal branes. Some features of T-duality and
implications for the finite temperature dual gauge theories are also discussed.
