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Typical Hamiltonian liquids display exponential "Lyapunov instability", alsocalled "sensitive dependence on initial conditions". Although Hamilton'sequations are thoroughly time-reversible, the forward and backward Lyapunovinstabilities can differ, qualitatively. In numerical work, the expectedforward/backward pairing of Lyapunov exponents is also occasionally violated.To illustrate, we consider many-body inelastic collisions in two spacedimensions. Two mirror-image colliding crystallites can either bounce, or not,giving rise to a single liquid drop, or to several smaller droplets, dependingupon the initial kinetic energy and the interparticle forces. The differencebetween the forward and backward evolutionary instabilities of these problemscan be correlated with dissipation and with the Second Law of Thermodynamics.Accordingly, these asymmetric stabilities of Hamilton's equations can providean "Arrow of Time". We illustrate these facts for two small crystallitescolliding so as to make a warm liquid. We use a specially-symmetrized form ofLevesque and Verlet's bit-reversible Leapfrog integrator. We analyzetrajectories over millions of collisions with several equally-spaced timereversals.

What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion