  The CoHSI (Conservation of Hartley-Shannon Information) distribution is at
the heart of a wide-class of discrete systems, defining (amongst other
properties) the length distribution of their components. Discrete systems such
as the known proteome, computer software and texts are all known to fit this
distribution accurately. In a previous paper, we explored the properties of
this distribution in detail. Here we will use these properties to show why the
average length of components in general and proteins in particular is highly
conserved, howsoever measured, demonstrating this on various aggregations of
proteins taken from the UniProt database. We will go on to define departures
from this equilibrium state, identifying fine structure in the average length
of eukaryotic proteins that result from evolutionary processes.
