  In this paper we present, in the context of Diaconis' paradigm, a general
method to detect the cutoff phenomenon. We use this method to prove cutoff in a
variety of models, some already known and others not yet appeared in
literature, including a chain which is non-reversible w.r.t. its stationary
measure. All the given examples clearly indicate that a drift towards the
opportune quantiles of the stationary measure could be held responsible for
this phenomenon. In the case of birth- and-death chains this mechanism is
fairly well understood; our work is an effort to generalize this picture to
more general systems, such as systems having stationary measure spread over the
whole state space or systems in which the study of the cutoff may not be
reduced to a one-dimensional problem. In those situations the drift may be
looked for by means of a suitable partitioning of the state space into classes;
using a statistical mechanics language it is then possible to set up a kind of
energy-entropy competition between the weight and the size of the classes.
Under the lens of this partitioning one can focus the mentioned drift and prove
cutoff with relative ease.
