  We propose a general quantitative scheme in which systems are given the
freedom to sacrifice energy equi-partitioning on the relevant time-scales of
observation, and have phase transitions by separating autonomously into ergodic
sub-systems (clusters) with different characteristic time-scales and
temperatures. The details of the break-up follow uniquely from the requirement
of zero entropy for the slower cluster. Complex systems, such as the
Sherrington-Kirkpatrick model, are found to minimise their free energy by
spontaneously decomposing into a hierarchy of ergodically equilibrating degrees
of freedom at different (effective) temperatures. This leads exactly and
uniquely to Parisi's replica symmetry breaking scheme. Our approach, which is
somewhat akin to an earlier one by Sompolinsky, gives new insight into the
physical interpretation of the Parisi scheme and its relations with other
approaches, numerical experiments, and short range models. Furthermore, our
approach shows that the Parisi scheme can be derived quantitatively and
uniquely from plausible physical principles.
