Thermodynamics for reduced models of polymer aggregation based on maximum entropy principle

Abstract

Polymeric aggregates play a significant role in biology and chemical engineering. In order to make a clear description of their underlying formation procedure, simplified models are crucial because the original mass-action equations involve numerous variables, complicating analysis and understanding. While the dynamical aspects of simplified models have been widely studied, their thermodynamic properties are less understood. In this study, we explore the Maximum Entropy Principle (MEP)-reduced models, initially developed for dynamical analysis, from a brand-new thermodynamic perspective. Analytical expressions, along with numerical simulations, demonstrate that the discrete MEP-reduced model strictly retains laws of thermodynamics, which holds true even when the aggregate size transits from discrete values to continuous real numbers. Our findings not only clarify the thermodynamic consistency between the MEP-reduced models and the original models of polymeric aggregates for the first time but also suggest avenues for future research into the model-reduction thermodynamics.