Optimizing Entropic Cluster Yields at Equilibrium Using Analytical Computation and Gradient-Based Methods

In self-assembly processes, the formation of desired structures is governed by both energetic and entropic factors, particularly when the system is at equilibrium. Traditional methods have typically focused on energy-driven optimization, minimizing potential energy or maximizing enthalpic interactions to drive assembly. In contrast, we present a novel approach that analytically computes the yield of entropic clusters, incorporating key entropic properties such as rotation, vibration, and translation. By utilizing automatic differentiation, we optimize system parameters—including the attractive potential between specific building blocks and their concentrations—via gradient descent to maximize or achieve target yields of specific monomeric structures. This method offers deeper insight into the role of entropy in the self-assembly process, providing an alternative to purely energy-based models. Furthermore, the entropic contributions help us understand how to control assembly pathways in complex molecular systems, such as those relevant for protein folding or drug delivery mechanisms. Our results highlight the potential of this framework to guide the design of molecular systems and materials, offering applications in fields such as drug development, nanotechnology, and materials science.