  We explore the statistical behavior of the discrete nonlinear Schroedinger
equation. We find a parameter region where the system evolves towards a state
characterized by a finite density of breathers and a negative temperature. Such
a state is metastable but the convergence to equilibrium occurs on astronomical
time scales and becomes increasingly slower as a result of a coarsening
processes. Stationary negative-temperature states can be experimentally
generated via boundary dissipation or from free expansions of wave packets
initially at positive temperature equilibrium.
