  The effect of non-Boltzmann energy distributions on the free propagation of
shock waves through a monoatomic gas is investigated via theory and simulation.
First, the non-Boltzmann heat capacity ratio $\gamma$, as a key property for
describing shock waves, is derived from first principles via microcanonical
integration. Second, atomistic molecular dynamics simulations resembling a
shock tube setup are used to test the theory. The presented theory provides
heat capacity ratios ranging from the well-known $\gamma = 5/3$ for Boltzmann
energy-distributed gas to $\gamma \to 1$ for delta energy-distributed gas. The
molecular dynamics simulations of Boltzmann and non-Boltzmann driven gases
suggest that the shock wave propagates about 9% slower through the
non-Boltzmann driven gas, while the contact wave appears to be about 4% faster
if it trails non-Boltzmann driven gas. The observed slowdown of the shock wave
through applying a non-Boltzmann energy distribution was found to be consistent
with the classical shock wave equations when applying the non-Boltzmann heat
capacity ratio. These fundamental findings provide novel insights into the
behavior of non-Boltzmann gases and might help to improve the understanding of
gas dynamical phenomena.
