Statistical complexity as a universal indicator of thermodynamic crossovers in ideal and van der Waals gases

We investigate the behavior of statistical complexity in interacting classical gases within the grand canonical ensemble. The analysis is carried out in an excluded-volume (van der Waals-type) framework, which captures the leading effects of repulsive interactions through a reduction of accessible phase space. A concise and self-contained formulation of statistical complexity is provided, emphasizing its interpretation as a measure of structural organization in the underlying probability distribution. We show that interaction effects induce a nontrivial reorganization of phase space, reflected in the behavior of statistical complexity as a function of thermodynamic parameters. In particular, the presence of excluded volume modifies the balance between disorder and structure, leading to qualitative changes absent in the ideal gas case. These features are traced back to the redistribution of accessible configurations imposed by finite-volume constraints. The results demonstrate that statistical complexity serves as a sensitive probe of interaction-induced structural changes. While the analysis is model-dependent, the observed behavior is robust within excluded-volume descriptions and highlights the role of repulsive interactions in shaping the statistical structure of the system. • Statistical complexity quantifies thermodynamic crossovers in classical gases. • Universal scaling law connects crossover temperatures with complexity growth. • Ideal and van der Waals gases are compared across arbitrary spatial dimensions. • Entropy reduction and disequilibrium enhancement reveal interaction effects. • Framework links information-theoretic measures with macroscopic thermodynamic behavior.