It is possible to unify certain kinetic properties of classical gases, as developedin Villani’s analysis of the Boltzmann equation, with quantum transport propertiesderived from the Bose–Hubbard model. The resulting “quantum-corrected Boltz-mann equation” incorporates bosonic statistics into the collision operator, leadingto a generalized H-theorem and entropy production functional. High-order pertur-bative expansions of the Mott phase of the Bose–Hubbard model are used to deriveexplicit corrections to macroscopic transport coefficients. We demonstrate that theGross–Pitaevskii equation emerges as a singular limit, and apply this innovativeconcept to astrophysical gases, revealing how superfluidity and quantum turbulencecan arise in neutron star interiors. This provides a bridge between classical andquantum gas dynamics and suggests new pathways for understanding turbulencein extreme cosmic environments.