We introduce the p-moment dual entropy for convex bodies containing the origin and establish for it isoperimetric-type inequalities associated with the Renyi entropy; the case p = n gives an isoperimetric inequality for the entropy itself. A differential formula is derived, leading to the corresponding entropy measure. We prove the existence of solutions to the associated Minkowski problem for p < 0, and show that for 1 < p ≤ n, this measure satisfies the pth subspace mass inequality within the class of origin-symmetric convex bodies. This is jointed work with Yin Leiqin.