  Decoherence effects at finite temperature (T) are examined for two manifestly
quantum systems: (i) Casimir forces between parallel plates that conduct along
different directions, and (ii) a topological Aharonov-Bohm (AB) type force
between fluxons in a superconductor. As we illustrate, standard path integral
calculations suggest that thermal effects may remove the angular dependence of
the Casimir force in case (i) with a decoherence time set by h/(k_{B} T) where
h is Plank's constant and k_{B} is the Boltzmann constant. This prediction may
be tested. The effect in case (ii) is due a phase shift picked by unpaired
electrons upon encircling an odd number of fluxons. In principle, this effect
may lead to small modifications in Abrikosov lattices. While the AB forces
exist at extremely low temperatures, we find that thermal decoherence may
strongly suppress the topological force at experimentally pertinent finite
temperatures. It is suggested that both cases (i) and (ii) (as well as other
examples briefly sketched) are related to a quantum version of the
fluctuation-dissipation theorem.
