Applying Villani to understand Cosmic Gas: Kinetics for Classical and Quantum Gas Dynamics: On the Emergence of Quantum Turbulence in Cosmic Media

It is possible to unify certain kinetic properties of classical gases, as developed
in Villani’s analysis of the Boltzmann equation, with quantum transport properties
derived from the Bose–Hubbard model. The resulting “quantum-corrected Boltz-
mann equation” incorporates bosonic statistics into the collision operator, leading
to 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 derive
explicit corrections to macroscopic transport coefficients. We demonstrate that the
Gross–Pitaevskii equation emerges as a singular limit, and apply this innovative
concept to astrophysical gases, revealing how superfluidity and quantum turbulence
can arise in neutron star interiors. This provides a bridge between classical and
quantum gas dynamics and suggests new pathways for understanding turbulence
in extreme cosmic environments.