Prethermalization with negative specific heat.

We study noncanonical relaxation in an aggregate of subsystems with negative specific heat. The Thirring instability drives the constituent subsystems towards the edges of their energy spectrum, so that the existence of a single adiabatic invariant results in structured noncanonical steady states that are spectacularly different from the grand-canonical prediction. For parameter regimes where this adiabatic invariance breaks down, the system exhibits prethermalization far away from integrability, with an unprecedented contrast between the prethermal- and thermal states.