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Lee-Yang zeros and phase transitions in nonequilibrium steady states

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R. A. Blythe, M. R. Evans

Statistical Mechanics · Submitted 19 Apr 2002

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

The authors' main claim We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

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arXiv IDcond-mat/0204421 (version 2)
Pith IDD5OWCV6C, Pith's permanent record of this paper and its review
CitationM. R. Evans, R. A. Blythe. "Lee-Yang zeros and phase transitions in nonequilibrium steady states." arXiv:cond-mat/0204421 (2002). https://pith.science/paper/D5OWCV6C
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,575 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.68 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

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 We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. background 0.66 0.50 0.05 unclear 0.82
s1 Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. method 0.49 0.28 0.06 asserted 0.99
s2 We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. result 0.46 0.96 0.11 asserted 1.00
s3 We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory. result 0.98 0.92 0.79 asserted 1.00

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

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper
  • Let us recall that a surprising connection between the $Q$-polynomial $Q^(0)(x)$ and the normalization of the stationary state has been discovered in [ref] , which relates the roots of the $Q$-polynomial $Q^(0)(x)$ and the Lee-Yang zeros studied in [ref] .

    Equivalent T-Q relations and exact results for the open TASEP · Expansion for small $μ$ · 0.81

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