  The issue of how time reversible microscopic dynamics gives rise to
macroscopic irreversible processes has been a recurrent issue in Physics since
the time of Boltzmann whose ideas shaped, and essentially resolved, such an
apparent contradiction. Following Boltzmann's spirit and ideas, but employing
Gibbs's approach, we advance the view that macroscopic irreversibility of
Hamiltonian systems of many degrees of freedom can be also seen as a result of
the symplectic non-squeezing theorem.
