  We discuss the entropy generation in quantum tunneling of a relativistic
particle under the influence of a time varying force with the help of squeezing
formalism. It is shown that if one associates classical coarse grained entropy
to the phase space volume, there is an inevitable entropy increase 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 barrier.
We suggest that the universe could have acquired its initial entropy in a
quantum squeeze from "nothing" and briefly discuss the implications of our
proposal.
