  Experiments motivated by predictions of quantum mechanics indicate
non-trivial correlations between spacelike-separated measurements. The
phenomenon is referred to as a violation of strong-locality and, after
Einstein, called ghostly action at a distance. An intriguing and previously
unasked question is how the evolution of an assembly of particles to
equilibrium-state relates to strong-locality. More specifically, whether, with
this respect, indistinguishable particles differ from distinguishable ones.
  To address the question, we introduce a Markov-chain based framework over a
finite set of microstates. For the first time, we formulate conditions needed
to obey the particle transport- and strong-locality for indistinguishable
particles.
  Models which obey transport-locality and lead to equilibrium-state are
considered. We show that it is possible to construct models obeying and
violating strong-locality both for indistinguishable particles and for
distinguishable ones. However, we find that only for distinguishable particles
strongly-local evolution to equilibrium is possible without breaking the
microstate-symmetry. This is the strongest symmetry one can impose and leads to
the shortest equilibration time.
  We hope that the results presented here may provide a new perspective on a
violation of strong-locality, and the developed framework will help in future
studies. Specifically they may help to interpret results on high-energy nuclear
collisions indicating a fast equilibration of indistinguishable particles.
