Thermal conductivity for stochastic energy exchange models

Makiko Sasada

RECORD

Thermal conductivity for stochastic energy exchange models

Makiko Sasada

Mathematical Physics · Submitted 27 Nov 2016

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

The authors' main claim In particular, we prove that the equality between the thermal conductivity and other static observables holds if and only if the model obeys the gradient condition.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,018 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider a class of stochastic models for energy transport and study relations between the thermal conductivity and some static observables, such as the static conductivity, which is defined as the contribution of static correlations in Green-Kubo formula. The class of models is a generalization of two specific models derived by Gaspard and Gilbert as mesoscopic dynamics of energies for two-dimensional and three-dimensional locally confined hard-discs. They claim some equalities hold between the thermal conductivity and several static observables and also conjecture that these equations are universal in the sense that they hold for mesoscopic dynamics of energies for confined particles interacting through hard-core collisions. In this paper, we give sufficient and necessary conditions for these equalities to hold in the class we introduce. In particular, we prove that the equality between the thermal conductivity and other static observables holds if and only if the model obeys the gradient condition. Since the gradient condition does not hold for models derived by Gaspard and Gilbert, our result implies a part of their claim is incorrect.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a class of stochastic models for energy transport and study relations between the thermal conductivity and some static observables, such as the static conductivity, which is defined as the contribution of static correlations in Green-Kubo formula.	contribution 0.70	0.78	0.03	asserted 0.93
s1	The class of models is a generalization of two specific models derived by Gaspard and Gilbert as mesoscopic dynamics of energies for two-dimensional and three-dimensional locally confined hard-discs.	background 0.67	0.14	0.02	asserted 1.00
s2	They claim some equalities hold between the thermal conductivity and several static observables and also conjecture that these equations are universal in the sense that they hold for mesoscopic dynamics of energies for confined particles interacting through hard-core collisions.	background 0.99	0.04	0.04	speculative 0.70
s3	In this paper, we give sufficient and necessary conditions for these equalities to hold in the class we introduce.	contribution 0.97	0.95	0.15	asserted 0.99
s4	In particular, we prove that the equality between the thermal conductivity and other static observables holds if and only if the model obeys the gradient condition.	result 1.00	0.95	0.83	asserted 1.00
s5	Since the gradient condition does not hold for models derived by Gaspard and Gilbert, our result implies a part of their claim is incorrect.	interpretation 0.96	0.86	0.53	asserted 0.94

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

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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 a class of stochastic models for energy transport and study relations between the thermal conductivity and some static observables, such as the static conductivity, which is defined as the contribution of static correlations in Green-Kubo formula. The class of models is a generalization of two specific models derived by Gaspard and Gilbert as mesoscopic dynamics of energies for two-dimensional and three-dimensional locally confined hard-discs. They claim some equalities hold between the thermal conductivity and several static observables and also conjecture that these equations are universal in the sense that they hold for mesoscopic dynamics of energies for confined particles interacting through hard-core collisions. In this paper, we give sufficient and necessary conditions for these equalities to hold in the class we introduce. In particular, we prove that the equality between the thermal conductivity and other static observables holds if and only if the model obeys the gradient condition. Since the gradient condition does not hold for models derived by Gaspard and Gilbert, our result implies a part of their claim is incorrect.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

4 arXiv papers cite this in 10 sentences

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

Papers citing it · 7 sentences without a confident label

Builds on it 1 paper

The present version is a substantial generalization of [ref] .

The gradient condition and the contribution of the dynamical part of Green-Kubo formula to the diffusion coefficient · Introduction · 0.99

Uses its method or tool 1 paper

Sasada's transposition of the variational formula to such a system [ref] provides an efficient instrument to obtain successive exact upper bounds for the heat transport coefficient, whose values can be extrapolated to infer an interval of confidence of the dynamic contribution to this quantity.

Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases · Conclusion · 0.96

Cites it as background 1 paper

Different variational methods have been applied to a number of lattice gas models in Refs. [ref] , while techniques similar to ours have been recently introduced to approximate the thermal conductivity for stochastic energy exchange models [ref] .

Variational calculation of transport coefficients in diffusive lattice gases · Conclusions · 0.90

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.