Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

Ryabov, Vladimir and Nerukh, Dmitry (2011). Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times. Chaos, 21 (3),

Abstract

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Publication DOI: https://doi.org/10.1063/1.3608125
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Chaos 21, 037113 (2011); and may be found at https://doi.org/10.1063/1.3608125
Uncontrolled Keywords: Applied Mathematics,Mathematical Physics,Physics and Astronomy(all),Statistical and Nonlinear Physics
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Related URLs: http://www.scopus.com/inward/record.url?scp=80053400717&partnerID=8YFLogxK (Scopus URL)
http://chaos.aip.org/resource/1/chaoeh/v21/i3/p037113_s1 (Publisher URL)
Published Date: 2011-09-30
Authors: Ryabov, Vladimir
Nerukh, Dmitry ( 0000-0001-9005-9919)

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