  Isoperimetric inequalities form a very intuitive yet powerful
characterization of the connectedness of a state space, that has proven
successful in obtaining convergence bounds. Since the seventies they form an
essential tool in differential geometry, graph theory and Markov chain
analysis. In this paper we use isoperimetric inequalities to construct a bound
on the convergence time of any local probabilistic evolution that leaves its
limit distribution invariant. We illustrate how this general result leads to
new bounds on convergence times beyond the explicit Markovian setting, among
others on quantum dynamics.
