Thermodynamic Modeling of Hashtag Dynamics for Social Media Clustering: A Maxwell-Boltzmann Approach

Social media hashtags function as critical organizational markers in digital discourse, yet traditional weighting methods fail to capture their dynamic significance across temporal and contextual dimensions. This paper presents a novel thermodynamic framework that conceptualizes social network activity as system “temperature”, applying statistical mechanics principles to model hashtag importance as process innovation. We establish mathematical foundations based on the Maxwell-Boltzmann distribution, providing an information-theoretic justification for dynamic hashtag weighting. Our approach incorporates activation thresholds and power-law scaling behaviors through a temperature-dependent function, with Simple Moving Average techniques implemented to stabilize temperature estimation, mathematically reducing variance by a factor of 1/N. Empirical evaluation using Twitter discourse from the US Presidential Election demonstrates unprecedented improvements in clustering performance: Silhouette Scores increased from 0.0126 to 0.9070 for Trump-related content and from 0.0105 to 0.8220 for Biden-related content, while Calinski-Harabasz Scores improved from 65.51 to nearly 98 million. These findings establish a rigorous mathematical bridge between thermodynamic systems and social media behavior, contributing to computational social science by providing a theoretical framework that significantly enhances discourse community detection in politically polarized environments. The approach enables more accurate identification of topic clusters, revealing distinct discourse patterns that conventional methods fail to capture.