Figure 10: Two snapshots of the collision of two 1600-particle slabs (periodic in the y direction, with height 20 and initial width 20 √ 3 / 4. The initial velocities, u$_{p}$ = ± 0 . 965 give twofold shock compression, followed by a nearly isentropic free expansion at the free surfaces. The thermodynamic irreversibility of the shockwave process has an interest indepen- dent of the definition of temperature and is worth futher study. The shock process it- self obeys purely Hamiltonian mechanics, and Liouville’s Theorem $^{20}$. Even so, by using Levesque and Verlet’s integer version of the leapfrog algorithm 21 the entire shockwave dy- namics can be precisely reversed, to the very last bit. The apparent paradox, a perfectly time-reversible but thermodynamically irreversible process, can most clearly be illustrated by simulating the (inelastic) collision of two zero-pressure blocks of fluid. The collision of the blocks, with velocities ± u$_{p}$ generates two shockwaves, with velocities ± ( u$_{s}$ − u$_{p}$ ). Two snapshots from such a simulation are shown in Figure 10. V. ACKNOWLEDGMENTS We appreciate stimulating comments from several colleagues: Paco Uribe, Vitaly Kuzkin, Howard Brenner, Michel Mareschal, Krzysztof Wojciechowski, and Jim Lutsko.