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This memoir honors the late Berni Julian Alder, who inspired both of us withhis pioneering development of molecular dynamics. Berni's work with TomWainwright, described in the 1959 Scientific American[1], brought Bill tointerview at Livermore in 1962. Hired by Berni, Bill enjoyed over 40 years'research at the Laboratory. Berni, along with Edward Teller, founded UC'sDepartment of Applied Science in 1963. Their motivation was to attract brightstudents to use the laboratory's unparalleled research facilities. In 1972Carol was offered a joint LLNL employee-DAS student appointment at Livermore.Bill, thanks to Berni's efforts, was already a Professor at DAS. Carol becameone of Bill's best students. Berni's influence was directly responsible for ourphysics collaboration and our marriage in 1989. The present work is devoted totwo early interests of Berni's, irreversibility and shockwaves. Berni and Tomstudied the irreversibility of Boltzmann's "H function" in the early 1950s[2].Berni called shockwaves the "most irreversible" of hydrodynamic processes[3].Just this past summer, in simulating shockwaves with time-reversible classicalmechanics, we found that reversed Runge-Kutta shockwave simulations yieldednonsteady rarefaction waves, not shocks. Intrigued by this unexpected result westudied the exponential Lyapunov instabilities in both wave types. Besides theRunge-Kutta and Leapfrog algorithms, we developed a precisely-reversiblemanybody algorithm based on trajectory storing, just changing the velocities'signs to generate the reversed trajectories. Both shocks and rarefactions wereprecisely reversed. Separate simulations, forward and reversed, provideinteresting examples of the Lyapunov-unstable symmetry-breaking modelssupporting the Second Law of Thermodynamics. We describe promising researchdirections suggested by this work.

Time-Symmetry Breaking in Hamiltonian Mechanics. II. A Memoir for Berni Julian Alder [1925-2020]