Practical implementations of quantum technology are limited by unavoidable
effects of decoherence and dissipation. With achieved experimental control for
individual atoms and photons, more complex platforms composed by several units
can be assembled enabling distinctive forms of dissipation and decoherence, in
independent heat baths or collectively into a common bath, with dramatic
consequences for the preservation of quantum coherence. The cross-over between
these two regimes has been widely attributed in the literature to the system
units being farther apart than the bath's correlation length. Starting from a
microscopic model of a structured environment (a crystal) sensed by two bosonic
probes, here we show the failure of such conceptual relation, and identify the
exact physical mechanism underlying this cross-over, displaying a sharp
contrast between dephasing and dissipative baths. Depending on the frequency of
the system and, crucially, on its orientation with respect to the crystal axes,
collective dissipation becomes possible for very large distances between
probes, opening new avenues to deal with decoherence in phononic baths