Using the concept of isomorphism, we provide a quantitative description of the thermodynamic characteristics of the Logistic, Bertalanffy, and Gompertz biological growth models. With the help of the entropy expressions derived from the isomorphic probabilistic models, we show that the Logistic, Bertalanffy, and Gompertz growth models have distinct thermodynamic characteristics, though they have similar sigmoid trajectories in the time domain. The entropic analysis further reveals that the Gompertz model corresponds to a completely open system, in which cells receive adequate nutrition and competition among cells can be neglected. We have also applied the present entropic analysis to the modeling of tumor growth. Our results suggest that the entropic expression provides a theoretical justification for using the Gompertz model for describing the development of tumor cell populations. The entropic analysis may play an important role in studying the mechanisms of different biological growth processes.