  We consider the thermodynamic and cosmological properties of brane gases in
the early universe. Working in the low energy limit of M-theory we assume the
universe is a homogeneous but anisotropic 10-torus containing wrapped 2-branes
and a supergravity gas. We describe the thermodynamics of this system and
estimate a Hagedorn temperature associated with excitations on the branes. We
investigate the cross-section for production of branes from the thermal bath
and derive Boltzmann equations governing the number of wrapped branes. A brane
gas may lead to decompactification of three spatial dimensions. To investigate
this possibility we adopt initial conditions in which we fix the volume of the
torus but otherwise assume all states are equally likely. We solve the
Einstein-Boltzmann equations numerically, to determine the number of dimensions
with no wrapped branes at late times; these unwrapped dimensions are expected
to decompactify. Finally we consider holographic bounds on the initial volume,
and find that for allowed initial volumes all branes typically annihilate
before freeze-out can occur.
