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).Comment: 12 pages; 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 Physic
