String thermodynamics in D-brane backgrounds

We discuss the thermal properties of string gases propagating in various D- brane backgrounds in the weak-coupling limit, and at temperatures close to the Hagedorn temperature. We determine, in the canonical ensemble, whether the Hagedorn temperature is limiting or non-limiting. This depends on the d imensionality of the D-brane, and the size of the compact dimensions. We fi nd that in many cases the non-limiting behaviour manifest in the canonical ensemble is modified to a limiting behaviour in the microcanonical ensemble and show that, when there are different systems in thermal contact, the en ergy flows into open strings on the 'limiting' D-branes of largest dimensio nality. Such energy densities may eventually exceed the D-brane intrinsic t ension. We discuss possible implications of this for the survival of Dp-bra nes with large values of p in an early cosmological Hagedorn regime. We als o discuss the general phase diagram of the interacting theory, as implied b y the holographic and black-hole/string correspondence principles.