Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-12-22
Physics
Condensed Matter
Statistical Mechanics
10 pages, 4 figures, for a special issue of Journal of Physics A, Lyapunov Analysis from Dynamical Systems Theory to Applicati
Scientific paper
Strong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet's bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of the forward and backward processes so as to identify those particles most intimately connected with the irreversibility described by the Second Law of Thermodynamics. Despite the time symmetry the fully-converged vectors associated with the largest Lyapunov exponents, forward and backward in time, are qualitatively different. There is a symmetry breaking equivalent to Time's Arrow in Newtonian shockwaves. That is, the largest Lyapunov exponents, forward and backward in time, do not display covariant behavior.
Hoover Carol G.
Hoover Wm G.
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