  Advanced kinetic theory with the Boltzmann-Curtiss equation provides a
promising tool for polyatomic gas flows, especially for fluid flows containing
inner structures, such as turbulence, polyatomic gas flows and others. Although
a Hamiltonian-based distribution function was proposed for diatomic gas flow, a
general distribution function for the generalized Boltzmann-Curtiss equations
and polyatomic gas flow is still out of reach. With assistance from Boltzmann's
entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic
gas flow is introduced. The corresponding governing equations at equilibrium
state are derived and compared with Eringen's morphing (micropolar) continuum
theory derived under the framework of rational continuum thermomechanics.
Although rational continuum thermomechanics has the advantages of mathematical
rigor and simplicity, the presented statistical kinetic theory approach
provides a clear physical picture for what the governing equations represent.
