Condensed Matter Physics, 2015, vol. 18, No. 1, p. 13003:113
DOI:10.5488/CMP.18.13003
arXiv:1405.2485
Title:
What is liquid? Lyapunov instability reveals symmetrybreaking irreversibilities hidden within Hamilton's manybody equations of motion
Author(s):

Wm.G. Hoover
(Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, Nevada 89833)
,


C.G. Hoover
(Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, Nevada 89833)

Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly timereversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numerical work, the expected forward/backward pairing of Lyapunov exponents is also occasionally violated. To illustrate, we consider manybody inelastic collisions in two space dimensions. Two mirrorimage colliding crystallites can either bounce, or not, giving rise to a single liquid drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces. The difference between the forward and backward evolutionary instabilities of these problems can be correlated with dissipation and with the Second Law of Thermodynamics. Accordingly, these asymmetric stabilities of Hamilton's equations can provide an "Arrow of Time". We illustrate these facts for two small crystallites colliding so as to make a warm liquid. We use a speciallysymmetrized form of Levesque and Verlet's bitreversible Leapfrog integrator. We analyze trajectories over millions of collisions with several equallyspaced time reversals.
Key words:
Lyapunov instability, exponent pairing, chaotic dynamics, irreversibility
PACS:
05.10.a, 05.45.a
