  By applying the Heisenberg's uncertainty principle for a macroscopic quantum
gas formed by gravitational waves an expression for the universal bound on the
entropy proposed by Bekenstein for any system of maximum radius R and total
energy E has been obtained. By using such expression, in the theoretical scheme
of the crystalline vacuum cosmic model, the low entropy value at the Big Bang
beginning, 1088k, is explained. According to our analysis the time arrow is
well defined and the theoretical time flow occurs only in one direction as
requested by the physical processes of gravitational stabilization of the
vacuum space crystalline structure around equilibrium conditions.
  PACS numbers: 65.50.+m, 97.60.Lf, 03.65.-w, 61.50.-f, 98.80.Ft, 04.20.-q
