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Thermodynamics of D-brane Probes 1

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). Based on talks presented at the midterm meeting of the TMR network "Physics beyond the standard model," held in Trieste in March 1999, and at the 1998 Corfu Summer Institute on Elementary Particle Physics. To appear in the proceedings. June 1999 Research supported in part by the National Science Foundation under grant PHY–96–02074, and in part by the EEC under the TMR contract ERBFMRX-CT96-0090.