Thermodynamics of the brane

The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a `melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations