Time-Irreversibility is Hidden Within Newtonian Mechanics

TL;DR

This paper presents a time-reversible simulation method based on Milne's algorithm to explore how irreversibility emerges in Newtonian mechanics, demonstrated through particle collision and oscillation experiments.

Contribution

It introduces a bit-reversible implementation of Milne's Predictor algorithm to simulate irreversible processes within Newtonian mechanics.

Findings

The algorithm accurately reproduces time-reversible dynamics.

It reveals the role of Lyapunov instability in irreversibility.

Demonstrates the emergence of time's arrow in classical 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".