  A quantum coordinate-entropy formulated in quantum phase space has been
recently proposed together with an entropy law that asserts that such entropy
can not decrease over time. The coordinate-entropy is dimensionless, a
relativistic scalar, and it is invariant under coordinate and CPT
transformations. We study here the time evolution of this entropy.
  We show that the entropy associated with coherent states evolving under a
Dirac Hamiltonian is increasing. However, for the collisions of two particles,
where each is evolving as a coherent state, as they come closer to each other
their spatial entanglement causes the total system's entropy to oscillate. We
augment time reversal with time translation and show that CPT with time
translation can transform particles with decreasing entropy for a finite time
interval into anti-particles with increasing entropy for the same finite time
interval.
  We then analyze the impact of the entropy law for the evolution scenarios
described above and explore the possibility that entropy oscillations trigger
the annihilation and the creation of particles.
