The Parisi scheme for equilibrium and the corresponding slow dynamics with
multithermalization – same temperature common to all observables, different
temperatures only possible at widely separated timescales — imply one another.
Consistency requires that two systems brought into infinitesimal coupling be
able to rearrange their timescales in order that all their temperatures match:
this time reorganisation is only possible because the systems have a set of
time-reparametrization invariances, that are thus seen to be an essential
component of the scenario.
