  We study non-canonical relaxation in a composite cold atoms system,
consisting of subsystems that possess negative microcanonical specific heat.
The system exhibits pre-thermalization far away from integrability due to the
appearance of a single adiabatic invariant. The Thirring instability drives the
constituent subsystems towards the edges of their allowed energy spectrum, thus
greatly enhancing the contrast between the prethermal state and the long time
thermal outcome.
