Time’s Arrow for Shockwaves; Bit - Reversible Lyapunov and “Covariant” Vectors; Symmetry Breaking

• Autorzy: Hoover W. G. , Hoover C. G.
• Języki publikacji: EN

Abstrakty

EN

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 nearby “satellite” trajectories. From the forward and backward processes we identify those particles most intimately connected with the irreversibility described by the Second Law of Thermodynamics. Despite the perfect time symmetry of the particle trajectories, the fully-converged vectors associated with the largest Lyapunov exponents, forward and backward in time, are qualitatively different. The vectors display a timesymmetry breaking equivalent to Time’s Arrow. That is, in autonomous Hamiltonian shockwaves the largest local Lyapunov exponents, forward and backward in time, are quite different.

Słowa kluczowe

EN

shockwaves; time reversibility; bit reversibility; Lyapunov instability

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2013
• Tom: Vol. 19, No. 2
• Strony: 69--75
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Hoover W. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

autor

Hoover C. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

Bibliografia

• [1] B.L. Holian, Wm.G. Hoover and H.A. Posch, Resolution of Loschmidt’s Paradox: the Origin of Irreversible Behavior in Reversible Atomistic Dynamics, Physical Review Letters 59, 10-13 (1987).
• [2] Wm.G. Hoover and C.G. Hoover, Time Reversibility, Computer Simulation, Algorithms and Chaos (World Scientific, Singapore, 2012).
• [3] Wm.G. Hoover, Liouville’s Theorems, Gibbs’ Entropy and Multifractal Distributions for Nonequilibrium Steady States, Journal of Chemical Physics 109, 4164-4170 (1998).
• [4] D.Levesque and L. Verlet, Molecular Dynamics and Time Reversibility, Journal of Statistical Physics 72, 519-537 (1993).
• [5] M. Romero-Bastida, D. Pazó, J M. López and M.A. Rodríguez, Structure of Characteristic Lyapunov Vectors in Anharmonic Hamiltonian Lattices, Physical Review E 82, 036205 (2010).
• [6] Wm.G. Hoover and C.G. Hoover, Three Lectures; NEMD, SPAM, and Shockwaves, pages 23-55 in Nonequilibrium Statistical Physics Today (Proceedings of the 11th Granada Seminar on Computational and Statistical Physics, 13-17 September 2010), P.L. Garrido, J. Marro and F. de los Santos, Editors (AIP Conference Proceedings #1332, Melville, New York, 2011).
• [7] Wm.G. Hoover and H.A. Posch, Direct Measurement of Equilibrium and Nonequilibrium Lyapunov Spectra, Physics Letters A 123, 227-230 (1987).
• [8] Wm.G. Hoover, C.G. Hoover and H.A. Posch, Dynamical Instabilities, Manifolds, and Local Lyapunov Spectra Far From Equilibrium, Computational Methods in Science and Technology (Poznan, Poland) 7, 55-65 (2001).
• [9] P.V. Kuptsov and U. Parlitz, Theory and Computation of Covariant Lyapunov Vectors, Journal of Nonlinear Science 22, 727-762 (2012); ariχv 1105.5228v3.
• [10] C. Dellago and Wm.G. Hoover, Are Local Lyapunov Exponents Continuous in Phase Space?, Physics Letters A 268, 330-334 (2000).
• [11] Wm.G. Hoover, C.G. Hoover and D.J. Isbister, Chaos, Ergodic Convergence, and Fractal Instability for a Thermostated Canonical Harmonic Oscillator, Physical Review E 63, 026209 (2001).