Ergodicity of the Martyna-Klein-Tuckerman Thermostat and the 2014 Ian Snook Prize

• Autorzy: Hoover W. G. , Hoover C. G.

Identyfikatory

DOI

10.12921/cmst.2015.21.01.002

• Języki publikacji: EN

Abstrakty

EN

Nosé and Hoover’s 1984 work showed that although Nosé and Nosé-Hoover dynamics were both consistent with Gibbs’ canonical distribution neither dynamics, when applied to the harmonic oscillator, provided Gibbs’ Gaussian distribution. Further investigations indicated that two independent thermostat variables are necessary, and often sufficient, to generate Gibbs’ canonical distribution for an oscillator. Three successful time-reversible and deterministic sets of twothermostat motion equations were developed in the 1990s. We analyze one of them here. It was developed by Martyna, Klein, and Tuckerman in 1992. Its ergodicity was called into question by Patra and Bhattacharya in 2014. This question became the subject of the 2014 Snook Prize. Here we summarize the previous work on this problem and elucidate new details of the chaotic dynamics in the neighborhood of the two fixed points. We apply six separate tests for ergodicity and conclude that the MKT equations are fully compatible with all of them, in consonance with our recent work with Clint Sprott and Puneet Patra.

Słowa kluczowe

EN

chaotic dynamics; time reversibility; ergodicity; fixed points

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2015
• Tom: Vol. 21, No. 1
• Strony: 5--10
• Opis fizyczny: Bibliogr. 13 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] S. Nosé, “A Unified Formulation of the Constant Temperature Molecular Dynamics Methods”, The Journal of Chemical Physics 81, 511-519 (1984).
• [2] S. Nosé, “A Molecular Dynamics Method for Simulations in the Canonical Ensemble”, Molecular Physics 52, 191-198 (1984).
• [3] W.G. Hoover, “Canonical Dynamics: Equilibrium PhaseSpace Distributions”, Physical Review A 31, 1695-1697 (1985).
• [4] W.G. Hoover and B.L. Holian, “Kinetic Moments Method for the Canonical Ensemble Distribution”, Physics Letters A 211, 253-257 (1996).
• [5] N. Ju and A. Bulgac, “Finite-Temperature Properties of Sodium Clusters”, Physical Review B 48, 2721-2732 (1993).
• [6] G.J. Martyna, M.L. Klein, and M. Tuckerman, “Nosé-Hoover Chains: the Canonical Ensemble via Continuous Dynamics”, The Journal of Chemical Physics 97, 2635-2643 (1992).
• [7] D. Kusnezov, A. Bulgac and W. Bauer, “Canonical Ensembles from Chaos”, Annals of Physics (NY) 204, 155-185 (1990).
• [8] A. Bulgac and D. Kusnezov, “Canonical Ensemble Averages from Pseudomicrocanonical Dynamics”, Physical Review A 42, 5045-5048 (1990).
• [9] P.K. Patra and B. Bhattacharya, “Non-Ergodicity of Nosé-Hoover Chain Thermostat in Computationally Achievable Time”, Physical Review E 90, 043304 (2014) = arχiv: 1407.2353 (2014).
• [10] Wm.G. Hoover and C.G. Hoover, “Ergodicity of a TimeReversibly Thermostated Harmonic Oscillator and the 2014 Ian Snook Prize”, Computational Methods in Science and Technology 20, 87-92 (2014).
• [11] W.G. Hoover, J.C. Sprott, P.K. Patra, and C.G. Hoover, “Deterministic Time-Reversible Thermostats: Chaos, Ergodicity, and the Zeroth Law of Thermodynamics”, arχiv 1501.03875 (2015), Molecular Physics (in press).
• [12] H.A. Posch, W.G. Hoover, and F.J. Vesely, “Canonical Dynamics of the Nosé Oscillator: Stability, Order, and Chaos”, Physical Review A 33, 4253-4265 (1986).
• [13] W.G. Hoover and H.A. Posch, “Direct Measurement of Equilibrium and Nonequilibrium Lyapunov Spectra”, Physics Letters A 123, 227-230 (1987).