In a sufficiently rarefied gas, the tools of standard
hydrodynamics, namely, the Navier-Stokes-Fourier equations
(based on Newton’s second law applied to fluid motion), no
longer apply. On the other hand, tracking the statistics of
individual molecules, as is done in Boltzmann’s kinetic equation
approach, is computationally prohibitive. Writing in Physical
Review Letters, Hans Christian Öttinger at the ETH in Zurich,
Switzerland, strengthens a description of rarefied gas flow that
is intermediate between these two extremes. Previous work showed
that Boltzmann’s kinetic equation can yield a set of moment
equations that describe the momentum of the gas and heat flux
within it. In his work, Öttinger looks to the laws of
nonequilibrium thermodynamics to provide the necessary
constraints on the equations. For example, entropy is conserved
in reversible processes and standard hydrodynamics is recovered
in the limiting case. The results could advance
efforts—particularly those based on numerical calculations—to
desc