With the rise of Large Language Models (LLMs), interest in simulating interaction dynamics has grown, raising questions about their validity as cognitive models of human discourse. While extensive research focuses on their performance in various applications, we aim to quantify LLM conversational processes akin to traditional human studies. By analyzing how convergence entropy evolves across different conversational tasks, we propose a framework for quantitatively assessing LLMs’ ability to exhibit specific features. This approach offers a pathway to characterizing LLMs for agent-based modeling and broader discourse analysis.