  The microscopic onset of irreversibility is finally becoming an experimental
subject. Recent experiments on microscopic open and even isolated systems have
measured statistical properties associated with entropy production, and
hysteresis-like phenomena have been seen in cold atom systems with dissipation
(i.e. effectively open systems coupled to macroscopic reservoirs). Here we show
how experiments on isolated systems of ultracold atoms can show dramatic
irreversibility like cooking an egg. In our proposed experiments, a slow
forward-and-back parameter sweep will sometimes fail to return the system close
to its initial state. This probabilistic hysteresis is due to the same
non-adiabatic spreading and ergodic mixing in phase space that explains
macroscopic irreversibility, but realized \textit{without} dynamical chaos;
moreover this fundamental mechanism quantitatively determines the probability
of return to the initial state as a function of tunable parameters in the
proposed experiments. Matching the predicted curve of return probability will
be a conclusive experimental demonstration of the microscopic onset of
irreversibility.

Quantum Gases;Statistical Mechanics