We obtain universal estimates on the convergence to equilibrium and the times
of coupling for continuous time irreducible reversible finite-state Markov
chains, both in the total variation and in the L^2 norms. The estimates in
total variation norm are obtained using a novel identity relating the
convergence to equilibrium of a reversible Markov chain to the increase in the
entropy of its one-dimensional distributions. In addition, we propose a
universal way of defining the ultrametric partition structure on the state
space of such Markov chains. Finally, for chains reversible with respect to the
uniform measure, we show how the global convergence to equilibrium can be
controlled using the entropy accumulated by the chain.Comment: 21 pages, 1 figur