  I argue that, in the chaotic version of string cosmology proposed recently,
classical and quantum effects generate, at the time of exit to radiation, the
correct amount of entropy to saturate a Hubble (or holography) entropy bound
(HEB) and to identify, within our own Universe, the arrow of time. Demanding
that the HEB be fulfilled at all times forces a crucial "branch change" to
occur, and the so-called string phase to end at a critical value of the
effective Planck mass, in agreement with previous conjectures.
