  We use path-integrals to derive a general expression for the semiclassical
approximation to the partition function of a one-dimensional quantum-mechanical
system. Our expression depends solely on ordinary integrals which involve the
potential. For high temperatures, the semiclassical expression is dominated by
single closed paths. As we lower the temperature, new closed paths appear,
including tunneling paths. The transition from single to multiple-path regime
corresponds to well-defined catastrophes. Tunneling sets in whenever they
occur. (Our formula fully accounts for this feature.)
