Strong shockwaves generate entropy quickly and locally. The Newton-Hamiltonequations of motion, which underly the dynamics, are perfectly time-reversible.How do they generate the irreversible shock entropy? What are the symptoms ofthis irreversibility? We investigate these questions using Levesque andVerlet's bit-reversible algorithm. In this way we can generate an entirelyimaginary past consistent with the irreversibility observed in the present. Weuse Runge-Kutta integration to analyze the local Lyapunov instability of theforward and backward processes so as to identify those particles mostintimately connected with the irreversibility described by the Second Law ofThermodynamics. Despite the perfect time symmetry of the particle trajectories,the fully-converged vectors associated with the largest Lyapunov exponents,forward and backward in time, are qualitatively different. The vectors displaya time-symmetry breaking equivalent to Time's Arrow. That is, in autonomousHamiltonian shockwaves the largest local Lyapunov exponents, forward andbackward in time, are quite different.
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