Mixing times for coagulation-fragmentation processes
There is a substantial literature on reversible Markov models for Coagulation
and Fragmentation of finite sets - see e.g.
But is is a (broad and vague) Open Problem to relate this to the
"Markov Chain Mixing Times" literature, specifically to get bounds on relaxation/mixing times
in terms of the model parameters.
Here are brief notes from an unposted section of Aldous-Fill RWG
on one model.
Another natural model is the finite analog of the split-merge transformation model in
P Diaconis, E Mayer-Wolf, O Zeitouni (2003).