  The abundances of anti-protons and protons are considered within
momentum-integrated Boltzmann equations describing Little Bangs, i.e.,
fireballs created in relativistic heavy-ion collisions. Despite of a large
anti-proton annihilation cross section we find a small drop of the ratio of
anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100
MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus
corroborating the solution of the previously exposed "ani-proton puzzle". In
contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a
long time in equilibrium resulting in an exceedingly small fraction. The
adiabatic path of cosmic matter in the phase diagram of strongly interacting
matter is mapped out.
