  We investigate the dynamics of pairs of Fermions and Bosons released from a
box and find that their populations have unique generic properties ensuing from
the axioms of quantum statistics and symmetries. These depend neither on the
specific equations of wave function propagation, such as Schr\"odinger,
Klein-Gordon, Dirac, nor on the specific potential involved. One surprising
finding is that after releasing the pairs, there are always more Boson than
Fermion pairs outside the box. Moreover, if the initial wave functions have the
same symmetry (odd or even), then there is a higher chance for a Boson than a
Fermion pair to escape from the trap in opposite directions, as if they repel
each other. We calculate the wave functions exactly, numerically, and
asymptotically for short time and demonstrate these generic results in the
specific case of particles released from an infinite well.

Quantum Physics;Statistical Mechanics;High Energy Physics - Theory