  Multi-epoch infrared photometry from Spitzer is used to monitor circumstellar
discs at white dwarfs, which are consistent with disrupted minor planets whose
debris is accreted and chemically reflected by their host stars. Widespread
infrared variability is found across the population of 37 stars with two or
more epochs. Larger flux changes occur on longer time-scales, reaching several
tens of per cent over baselines of a few years. The canonical model of a
geometrically thin, optically thick disc is thus insufficient, as it cannot
give rise to the observed behaviour. Optically thin dust best accounts for the
variability, where collisions drive dust production and destruction. Notably,
the highest infrared variations are seen in systems that show Ca II emission,
supporting planetesimal collisions for all known debris discs, with the most
energetic occurring in those with detected gaseous debris. The sample includes
the only polluted white dwarf with a circumbinary disc, where the signal of the
day-night cycle of its irradiated substellar companion appears diluted by dust
emission.
