  We analyze the dynamics of intersecting D3/D3' brane system overlapping in
1+1 dimensions, in a holographic treatment where $N$ D3-branes are manifested
as anti-de-Sitter Schwartzschild geometry, and the D3'-brane is treated as a
probe. We extract the thermodynamic equation of state from the set of embedding
solutions, and analyze the stability at the perturbative and the
non-perturbative level. We review a systematic procedure to resolve local
instabilities and multi-valuedness in the equations of state based on classic
ideas of convexity in microcanonical ensumble. We then identify a run-away
behavior which was not noticed previously for this system.
