Can anyone shed some light (whats it all about?) on the Entropy condition and methods used to ensure that the Entropy condition is not violated in solutions to certain hyperbolic pde's?

Thanks.

Right from scratch only on a basic level:

To most hyperbolic PDEs, there is more than one weak solution. But we are only interested in the one that represents the physics. Some solutions are unphysical in that they decrease entropy. To outrule those and to pick one solution as the one that we seek, entropy conditions are used. These single out one of the several weak solutions to the PDE. That's the general idea. On the discrete level, you have to design a method that automatically enforces a discrete version of the entropy condition. For more, consult your favorite book on numerical methods for conservation laws or the papers by Kuzhnezov and by Lax.