We discuss the entropy generation in quantum tunneling of a relativistic pa
rticle under the influence of a time-varying force with the help of squeezi
ng formalism. It is shown that if one associates classical coarse grained e
ntropy to the phase space volume, there is an inevitable entropy growth due
to the changes in position and momentum variances. The entropy change can
be quantified by a. simple expression Delta S = ln cosh 2r, where r is the
squeeze parameter measuring the "height" and "width" of the potential barri
er. We suggest that thc: universe could have acquired its initial entropy i
n a quantum squeeze from "nothing" and briefly discuss the implications of
our proposal.