Abstract
Observations of the evolution of the galaxy cluster X-ray luminosity function suggest that the entropy of the intracluster 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 intracluster 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 intracluster 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.