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Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics

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C. P. Dettmann, G. P. Morriss (UNSW, Sydney, Australia)

chao-dyn · Submitted 10 Dec 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this form it is possible to prove the conjugate pairing rule for Lyapunov exponents of this system.

how it is stated · asserted 0.52 read the record →

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arXiv IDchao-dyn/9612018 (version 1)
Pith IDYKJC5IDR, Pith's permanent record of this paper and its review
CitationAustralia), C. P. Dettmann, G. P. Morriss (UNSW, Sydney. "Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics." arXiv:chao-dyn/9612018 (1996). https://pith.science/paper/YKJC5IDR
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,342 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The Nose Hamiltonian is adapted, leading to a derivation of the Nose-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the external reservoir is treated on the same footing as those of the rest of the system. In this form it is possible to prove the conjugate pairing rule for Lyapunov exponents of this system.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The Nose Hamiltonian is adapted, leading to a derivation of the Nose-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the external reservoir is treated on the same footing as those of the rest of the system. contribution 0.58 0.88 0.21 asserted 1.00
s1 In this form it is possible to prove the conjugate pairing rule for Lyapunov exponents of this system. result 0.95 0.83 0.64 asserted 0.52

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The Nose Hamiltonian is adapted, leading to a derivation of the Nose-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the external reservoir is treated on the same footing as those of the rest of the system. In this form it is possible to prove the conjugate pairing rule for Lyapunov exponents of this system.

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