Statistical Ensemble Theory of Gompertz Growth Model

Abstract

An ensemble formulation for the Gompertz growth function within the framework of statistical mechanics is presented, where the two growth parameters are assumed to be statistically distributed. The growth can be viewed as a self-referential process, which enables us to use the Bose-Einstein statistics picture. The analytical entropy expression pertain to the law can be obtained in terms of the growth velocity distribution as well as the Gompertz function itself for the whole process.

Keywords

• Gompertz function
• tumour growth
• Bose-Einstein statistics
• entropy