  In the standard model of cosmology, the Universe began its expansion with an
anomalously low entropy, which then grew dramatically to much larger values
consistent with the physical conditions at decoupling, roughly 380,000 years
after the Big Bang. There does not appear to be a viable explanation for this
`unnatural' history, other than via the generalized second law of
thermodynamics (GSL), in which the entropy of the bulk, S_bulk, is combined
with the entropy of the apparent (or gravitational) horizon, S_h. This is not
completely satisfactory either, however, since this approach seems to require
an inexplicable equilibrium between the bulk and horizon temperatures. In this
paper, we explore the thermodynamics of an alternative cosmology known as the
R_h=ct universe, which has thus far been highly successful in resolving many
other problems or inconsistencies in LCDM. We find that S_bulk is constant in
this model, eliminating the so-called initial entropy problem simply and
elegantly. The GSL may still be relevant, however, principally in selecting the
arrow of time, given that S_h ~ t^2 in this model.
