Quantum Maximum Entropy Principle and Quantum Statistics in Extended Thermodynamics

By using a functional of the reduced density matrix, a formulation of quantum maximum entropy principle (QMEP) for the fractional exclusion statistics (FES) is proposed. In this way, compatibly with the uncertainty principle, we include a nonlocal description for the anyonic systems satisfying FES. By considering the Wigner formalism, we present a general scheme to develop a closed quantum hydrodynamic models in the framework of Extended Thermodynamics. Accordingly, the QMEP including FES is here asserted as the most advanced formulation of the fundamental principle of quantum statistical mechanics.