Correlation induced by Tsallis’ nonextensivity

In Tsallis’ generalized statistical mechanics, correlation is induced by nonextensivity even if the microscopic degrees of freedom are dynamically independent. Here, using the classical ideal gas model, the generalized variance, covariance and correlation coefficient regarding the particle energies are calculated and their properties discussed. It is shown that the correlation is suppressed for a large number of particles. This demonstrates the validity of the independent particle picture for a dense gas rather than for a dilute gas. It is also found that, in the thermodynamic limit, the correlation again vanishes and the generalized variance exhibits a power-law behavior with respect to the particle number density. Relevance of these results to the zeroth law of thermodynamics in nonextensive statistical mechanics is pointed out.