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 quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with 0-brane charge. This result is in accordance with the duality conjectured by Itzhaki, Maldacena, Sonnenschein, and Yankielowicz [Phys. Rev. D 58, 046004 (1998)]. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly coupled quantum mechanics.