Quantization of Boltzmann Entropy: Pairs and Correlation Function

We consider the Gibbs statistical ensemble. We introduce the statistical-weight operator $\widehat\Gamma$, construct the entropy operator $\widehat S$ of the ensemble using the Boltzmann formula $\widehat S=\ln\widehat\Gamma$ and define the free-energy operator. We find asymptotic expressions for free-energy eigenvalues with pair correlations taken into account in the limit as the number of systems in the ensemble tends to infinity.