Black hole thermodynamics from calculations in strongly coupled gauge theory

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large-N limit. The entropy of the qu antum mechanics calculated using this approximation agrees well with the Be kenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by It zhaki, Maldacena, Sonnenschein and Yankielowicz. Our approximation scheme p rovides a model for the density matrix which describes a black hole in the strongly-coupled quantum mechanics.