  Sinai chaos is characterized by exponential divergence between neighboring
trajectories of a point billiard. If the repulsive potential of the
finite-diameter fixed particle in the middle of the table is made smooth, the
Sinai divergence persists with finite measure. So it does if the smooth
potential is made attractive. So it still does if the potential is in addition
made time-dependent (periodic). Then a systematic decrease in energy of the
moving particle can be predicted to occur in both time directions for a long
time. If so, classical entropy acquires an analog in real space.
