Time-Irreversibility is Hidden Within Newtonian Mechanics

Abstract

We develop a bit-reversible implementation of Milne's Fourth-order Predictor algorithm so as to generate precisely time-reversible simulations of irreversible processes. We apply our algorithm to the collision of two zero-temperature Morse-potential balls, which collide to form a warm liquid oscillating drop. The oscillations are driven by surface tension and damped by the viscosities. We characterize the "important" Lyapunov-unstable particles during the collision and equilibration phases in both time directions to demonstrate the utility of the Milne algorithm in exposing "Time's Arrow".

21 pages with ten figures prepared for Daan Frenkel's Festschrift celebrating his 70th Birthday

References in corpus (2)

• Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient
• What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion