DOI: 10.1063/1.166315. The conjugate-pairing rule for non-Hamiltonian systems

The conjugate-pairing rule for non-Hamiltonian systems

10.1063/1.166315

Crossref journal-article

AIP Publishing

Chaos: An Interdisciplinary Journal of Nonlinear Science (317)

Abstract

In systems that satisfy the Conjugate Pairing Rule (CPR), the spectrum of Lyapunov exponents is symmetric. The sum of each conjugate pair of exponents is identical. Since in dissipative systems the sum of all the exponents is the entropy production divided by Boltzmann’s constant, the calculation of transport coefficients from the Lyapunov exponents is greatly simplified in systems that satisfy CPR. Sufficient conditions for CPR are well known: the underlying adiabatic dynamics should be symplectic. However, the necessary conditions for CPR are not known. In this paper we report on the results of computer simulations which shed light on the necessary conditions for the CPR to hold. We provide, for the first time, convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the CPR, even in the thermodynamic limit. In spite of this it appears that the sum of the maximal exponents is equal to the entropy production per degree of freedom. Thus it appears that the shear viscosity can still be calculated using the standard viscosity algorithm by summing the maximal pair of exponents.

Bibliography

Searles, D. J., Evans, D. J., & Isbister, D. J. (1998). The conjugate-pairing rule for non-Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 8(2), 337â349.

Authors 3

Debra J. Searles (first)
Denis J. Evans (additional)
Dennis J. Isbister (additional)

References 29 Referenced 25

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{'key': '2024020122361569400_r12'}
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{'key': '2024020122361569400_r18'}
{'key': '2024020122361569400_r19', 'first-page': '147', 'article-title': 'Mathematics and computers in simulation: Non-standard applications of computer science', 'volume': '45', 'year': '1998', 'journal-title': 'Math. Comput. Simulation'} / Math. Comput. Simulation / Mathematics and computers in simulation: Non-standard applications of computer science (1998)
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{'key': '2024020122361569400_r24'}

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:43 a.m.)
Deposited	1 year, 6 months ago (Feb. 1, 2024, 6:21 p.m.)
Indexed	1 month, 2 weeks ago (July 7, 2025, 4:24 a.m.)
Issued	27 years, 2 months ago (June 1, 1998)
Published	27 years, 2 months ago (June 1, 1998)
Published Print	27 years, 2 months ago (June 1, 1998)

Funders 0

None

BibTeX

@article{Searles_1998, title={The conjugate-pairing rule for non-Hamiltonian systems}, volume={8}, ISSN={1089-7682}, url={http://dx.doi.org/10.1063/1.166315}, DOI={10.1063/1.166315}, number={2}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP Publishing}, author={Searles, Debra J. and Evans, Denis J. and Isbister, Dennis J.}, year={1998}, month=jun, pages={337–349} }

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