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We relate a Dp or NS-brane with D0-brane charge smeared over its worldvolumeto the system with no D0-charge. This allows us to generalise Reall's partialproof of the Gubser-Mitra conjecture. We show explicitly for specific examplesthat the dynamical instability coincides with thermodynamic instability in theensemble where the D0-brane charge can vary. We also comment on consistencychecks of the conjecture for more complicated systems, using the example of theD4 with F1 and D0 charges smeared on its worldvolume.Comment: 16 pages, 1 figure, v2: small error correcte

Smeared D0 charge and the Gubser–Mitra conjecture