  Systems evolving according to the standard concept of biological or
technological evolution are often described by catalytic evolution equations.
We study the structure of these equations and find a deep relationship to
classical thermodynamics. In particular we can demonstrate the existence of
several distinct phases of evolutionary dynamics: a phase of fast growing
diversity, one of stationary, finite diversity, and one of rapidly decaying
diversity. While the first two phases have been subject to previous work, here
we focus on the destructive aspects - in particular the phase diagram - of
evolutionary dynamics. We further propose a dynamical model of diversity which
captures spontaneous creation and destruction processes fully respecting the
phase diagrams of evolutionary systems. The emergent timeseries show a Zipf law
in the diversity dynamics, which is e.g. observable in actual economical data,
e.g. in firm bankruptcy data. We believe the present model is a way to cast the
famous qualitative picture of Schumpeterian economic evolution, into a
quantifiable and testable framework.
