  Shockwaves provide a useful and rewarding route to the nonequilibrium
properties of simple fluids far from equilibrium. For simplicity, we study a
strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear
transport properties makes plain the connection between the observed local
hydrodynamic variables (like the various gradients and fluxes) and the chosen
recipes for defining (or "measuring") those variables. The range over which
nonlocal hydrodynamic averages are computed turns out to be much more
significant than are the other details of the averaging algorithms. The results
show clearly the incompatibility of microscopic time-reversible
cause-and-effect dynamics with macroscopic instantaneously-irreversible models
like the Navier-Stokes equations.
