  In this article, we consider the Chew, Goldberger \& Low (CGL) plasma flow
equations, which is a set of nonlinear, non-conservative hyperbolic PDEs
modelling anisotropic plasma flows. These equations incorporate the double
adiabatic approximation for the evolution of the pressure, making them very
valuable for plasma physics, space physics and astrophysical applications. We
first present the entropy analysis for the weak solutions. We then propose
entropy-stable finite-difference schemes for the CGL equations. The key idea is
to rewrite the CGL equations such that the non-conservative terms do not
contribute to the entropy equations. The conservative part of the rewritten
equations is very similar to the magnetohydrodynamics (MHD) equations. We then
symmetrize the conservative part by following Godunov's symmetrization process
for MHD. The resulting equations are then discretized by designing entropy
conservative numerical flux and entropy diffusion operator based on the entropy
scaled eigenvectors of the conservative part. We then prove the semi-discrete
entropy stability of the schemes for CGL equations. The schemes are then tested
using several test problems derived from the corresponding MHD test cases.
