  In a previous paper, we discussed simple examples like particle on a circle
and molecules to argue that mixed states can arise from anomalous symmetries.
This idea was applied to the breakdown (anomaly) of color SU(3) in the presence
of non-abelian monopoles. Such mixed states create entropy as well.
  In this article, we extend these ideas to the topological geons of Friedman
and Sorkin in quantum gravity. The "large diffeos" or mapping class groups can
become anomalous in their quantum theory as we show. One way to eliminate these
anomalies is to use mixed states, thereby creating entropy. These ideas may
have something to do with black hole entropy as we speculate.
