  Soft particulate media include a wide range of systems involving athermal
dissipative particles both in non-living and biological materials.
Characterization of flows of particulate media is of great practical and
theoretical importance. A fascinating feature of these systems is the existence
of a critical rigidity transition in the dense regime dominated by highly
intermittent fluctuations that severely affects the flow properties. Here, we
unveil the underlying mechanisms of rare fluctuations in soft particulate
flows. We find that rare fluctuations have different origins above and below
the critical jamming density and become suppressed near the jamming transition.
We then conjecture a time-independent local fluctuation relation, which we
verify numerically, and that gives rise to an effective temperature. We discuss
similarities and differences between our proposed effective temperature with
the conventional kinetic temperature in the system by means of a universal
scaling collapse.
