  Observations of the evolution of the galaxy cluster X-ray luminosity function
suggest that the entropy of the intra-cluster medium plays a significant role
in determining the development of cluster X-ray properties. I present a
theoretical framework in which the evolution of the entropy of the central
intra-cluster gas is explicitly taken into account. The aim of this work is to
develop a theoretical context within which steadily improving measurements of
the X-ray luminosities and temperatures of distant galaxy clusters can be
interpreted. I discuss the possible range of entropy evolution parameters and
relate these to the physical processes heating and cooling the intra-cluster
medium. The practical application of this work is demonstrated by combining
currently available evolutionary constraints on the X-ray luminosity function
and the luminosity--temperature correlation to determine the best-fitting model
parameters.
