Thanks to David for clarifying my somewhat hastily written item.
I did want to indicate that minimization of potential energy alone
is only a valid criterion for the approach to equilibrium of a
still smaller set of systems than we were considering. I also did
want to make the point that sometimes the approach is not to *the*
minimum of some quantity, but rather to *a* nearby (in phase space
terms) minimum of that quantity. (Replace "minimum" by "maximum"
if appropriate to the quantity in question, e.g. the entropy of
the system.) Every system has an ultimate thermodynamic fate as a
black hole, even if the only way to get there is via QM tunneling.
Incidentally, the general name for the kind of process where
equilibrium is approached through dissipation is "relaxation".
Introduction and proper use of that term will save lots of typing
in these discussions.