  This is a companion paper of our previous work [1] where we studied the
thermodynamics and phase structure of asymptotically flat black $p$-branes in a
cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we
study the thermodynamics and phase structure of the same in a grand canonical
ensemble. Since the boundary data in two cases are different (for the grand
canonical ensemble boundary potential is fixed instead of the charge as in
canonical ensemble) the stability analysis and the phase structure in the two
cases are quite different. In particular, we find that there exists an analog
of one-variable analysis as in canonical ensemble, which gives the same
stability condition as the rather complicated known (but generalized from black
holes to the present case) two-variable analysis. When certain condition for
the fixed potential is satisfied, the phase structure of charged black
$p$-branes is in some sense similar to that of the zero charge black $p$-branes
in canonical ensemble up to a certain temperature. The new feature in the
present case is that above this temperature, unlike the zero-charge case, the
stable brane phase no longer exists and `hot flat space' is the stable phase
here. In the grand canonical ensemble there is an analog of Hawking-Page
transition, even for the charged black $p$-brane, as opposed to the canonical
ensemble. Our study applies to non-dilatonic as well as dilatonic black
$p$-branes in $D$ space-time dimensions.
