Statistical complexity as indicator of the classical–quantum crossover

Abstract

We explore the behavior of statistical complexity as a possible indicator of the crossover between classical and quantum behaviors in thermo-dynamic systems. Using the López-Ruiz, Mancini, and Calbet statistical complexity measure C, along with the disequilibrium D, we analyzeboth the ideal and van der Waals gases as they approach regimes where quantum statistics become significant. We find that C reaches a well-defined maximum at a characteristic temperature Tc in all cases considered. Interestingly, the numerical value of C at this temperature is thesame across these models. While the underlying reason for this behavior is not yet fully understood, it suggests that statistical complexity maycapture structural changes in the system’s phase space that are associated with the emergence of quantum effects. The shift of Tc in the vander Waals case, depending on the excluded volume parameter b, reflects the influence of interactions on this crossover behavior. These resultsindicate that C might serve as a useful proxy for detecting the changes in the statistical structure of many-body systems as they transition fromclassical to quantum regimes.