Thermodynamics of D-brane Probes

We discuss the dynamics and thermodynamics of particle and D-brane probes moving in non-extremal black hole/brane backgrounds. When a probe falls from asymptotic infinity to the horizon, it transforms its potential energy into heat, $TdS$, which is absorbed by the black hole in a way consistent with the first law of thermodynamics. We show that the same remains true in the near-horizon limit, for BPS probes only, with the BPS probe moving from AdS infinity to the horizon. This is a quantitative indication that the brane-probe reaching the horizon corresponds to thermalization in gauge theory. It is shown that this relation provides a way to reliably compute the entropy away from the extremal limit (towards the Schwarzschild limit).