Due to its intrinsic complexity, a complete mathematical description of the cell cycle appears a difficult task. Nevertheless, a preliminary analysis, based on molecular biology, can help in clarifying what are the reliable tools for a quantitative approach. In a previous paper [Physica A 321 (3-4) (2003) 587], the steps to be followed to formulate a metabolic statistical thermodynamics have been established. Here we present a simple mathematical model for the interaction of CyclinB and Cdh1 [The Cell Cycle. An Introduction, Oxford University Press, New York, 1993], with the aim of analysing the properties of the system from a thermodynamic viewpoint. The model is shown to define the Gibbs phase integral of the system and the general Gibbs energy function is obtained. This, together with the analogue of the temperature, defines the working tools indispensable for the formulation of a metabolic statistical thermodynamic-like theory. © 2003 Elsevier B.V. All rights reserved.