The Bhatnagar-Gross-Krook (BGK) Boltzmann equation with the Maxwellian-Boltzmann-type equilibrium state leads to the set of thermo-hydrodynamic equations such as the continuity, the Navier-Stokes, and the heat-transfer equations in the scaling limit. In this study, using an analytical technique of the kinetic generator, we employ a non-local formulation for the equilibrium state, called a quasi-equilibrium state, to derive the thermo-hydrodynamic equations with flexible choices of transport coefficients and the equation of state (EOS). It is formulated with the non-local macroscopic quantities so that the long-range interaction is explicitly included. According to the new formulation, the consistency with the conservation laws, the Boltzmann H-theorem, and the fluctuation-dissipation theorem is investigated.
