STATISTICAL-MECHANICS OF D0-BRANES AND BLACK-HOLE THERMODYNAMICS

We consider a system of D0-branes in toroidally compactified space wit h interactions described by a Born-Infeld-type generalisation of the l eading v(2) + v(4) = r(D-4) terms (D is the number of non-compact dire ctions in M-theory, including the longitudinal one). This non-linear a ction can be interpreted as an all-loop large N super Yang-Mills effec tive action and has a remarkable scaling property. We first study the classical dynamics of a brane probe in the field of a central brane so urce and observe the interesting difference between the D = 5 and D > 5 cases: for D > 5 the center acts as a completely absorbing black hol e of effective size proportional to a power of the probe energy, while for D = 5 there is no absorption for any impact parameter. A similar dependence on D is found in the behaviour of the Boltzmann partition f unction Z of an ensemble of D0-branes. For D = 5 (i.e. for compactific ation on 6-torus) Z is convergent at short distances and is analogous to the ideal gas one. For D > 5 the system has short-distance instabil ity. For sufficiently low temperature Z is shown to describe the therm odynamics of a Schwarzschild black hole in D > 5 dimensions, supportin g recent discussions of black holes in Matrix theory.