Fluid-dynamic limit of the Enskog equation with the guaranteed H-theorem

The fluid-dynamic limit of the Enskog equation is discussed based on the Chapman–Enskog method as described in [Takahashi and Takata, arXiv:2507.01341]. The Enskog equation is a kinetic equation that describes the behavior of dense or real gases. A modified version of the Enskog equation was recently proposed in [Takata and Takahashi, Phys. Rev. E 111, 065108 (2025)], and its H-theorem is guaranteed in contrast to the original Enskog equation. Macroscopic fluid equations are derived from a kinetic equation by performing an asymptotic expansion, which is referred to as the fluid-dynamic limit. It is shown that the modified version recovers the same fluid-dynamic description of dense gases as the original one, at least up to the level of the Navier–Stokes–Fourier equations. Since the original Enskog equation is known to recover the fluid-dynamical transport properties well, this result implies that the modified version of the Enskog equation provides consistent descriptions both thermodynamically and fluid-dynamically.