  The statistical properties of physical systems in thermal equilibrium are
blatantly different from their far-from-equilibrium counterparts. In the
latter, fluctuations often dominate the dynamics and might cluster in ordered
patterns in the form of dissipative coherent structures. Here, we study the
transition of a cold atomic cloud, driven close to a sharp electronic
resonance, from a stable to a turbulent phase. From the atomic density
distribution -- measured using a spatially-resolved pump-probe technique -- we
have computed the Shannon entropy on two different basis sets. Information
compression, corresponding to a minimum in the Shannon entropy, has been
observed at criticality, where the system fluctuations organize into high-order
(low-entropy) patterns. Being independent of the representation used, this
feature is a property shared by a vast class of physical systems undergoing
phase transitions.
