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Peer-Review Record

Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures

Entropy 2021, 23(12), 1630;
Reviewer 1: Anonymous
Reviewer 2: Zhongwei Zhang
Entropy 2021, 23(12), 1630;
Received: 3 November 2021 / Revised: 28 November 2021 / Accepted: 1 December 2021 / Published: 3 December 2021

Round 1

Reviewer 1 Report



The contribution of the report to the body of knowledge is significant and novel. The aim and objectives of the study are within the scope of Journal. However, the present form of the report needs revision. The author should improve the following points in the revised version before acceptance.

  • The Abstract should contain answers to the following questions: What problem was studied and why is it important? What methods were used? What are the important results? What conclusions can be drawn from the results? What is the novelty of the work and where does it go beyond previous efforts in the literature? Please include specific and quantitative results in your Abstract, while ensuring that it is suitable for a broad audience.
  • Have you employed any assumptions? Please explain. More explanation is needed on model and the assumptions.
  • You should add appropriate references for equation 1, 2 and 11
  • How the equations (4) have been derived? It should include a brief discussion or at least support of any previous study, so that readers can understand it quickly.
  • It is recommended the authors try to explain the novelty of the paper as clear as possible and explain the research gap they are trying to fill.
  • Mathematical modeling is also not well presented. Every equation must be named and discussed. Model simplifications must be discussed and all variables must be defined.
  • Revise the introduction such that each paragraph shall present the meaning of a concept/keyword. Each paragraph must present at least three theoretical reviews on the same concept/keyword. Also, the same paragraph should articulate at least three published results on the major concept/keyword. This would make the introduction suitable to announce the title, aim, objectives, and attract the interest of the readers. The introduction section can be supported with some more recent related literature especially since all references are not relatively recent. Introduction section can be supported with some more recent related literature


Author Response

We thank the reviewer for their comments. Accordingly, we rewrote the abstract, and added references to equation 11. Equations 1 and 2 are however my model and it describes an anharmonic hamiltonian.
    More explanations are now provided to the best of our ability to make the modeling more clear. Everywhere an assumption is introduced, it has been discussed. Simplifications/approximations to the solution come at the end of the paper, and they are discussed in the conclusion section.

Reviewer 2 Report

Please see the comments in the attached file.

Comments for author File: Comments.pdf

Author Response

We thank the reviewer for their comments. 
We have clarified in the revised version (see also revised abstract) that the novelty of this work is in showing that the quartic anharmonicity needs to be included in the formalism. Previous approaches of Mingo (4), Wang(5), Volz(7), and Tian(6) all only included the cubic term, which has a second-order contribution, while the quartic term has the leading order effect, and needs to be included first.
To second-order, we obtain similar results as the cited authors. The difference is our derivation which was classical and based on the equation of motion method, and thus supposedly simpler. I must mention that the full derivation in the previous papers using the Keldysh formalism is absent in the papers as they use the standard results already established by Keldysh method.
I realize that there are too many equations for the reader to follow, but I am including all derivations for completeness. The main point however is that adding the quartic contribution is needed and simple enough that it should always be done before adding the cubic part.

Regarding the application to a simple system, this is the obect of a coming paper. even for a linear chain the inclusion of cubic terms to second-order is tedious, while the quartic effect is trivial to show, but it is not comparable to anything. 

Finally, the extraction for force constants from NEMD, i.e. fitting Forces F_i with a harmonic model Sum_j phi_ij y_j is a simple least squares fitting problem which I and many others have done in the past. Many forse-displacements snapshots are of course needed to generate enough equations to solve for the unknown force constants. See refs 22 (Esfarjani, K.; Stokes, H.T. Method to extract anharmonic force constants from first principles calculations.Phys. Rev. B2008,77, 144112) and 23 (Tadano,  T.;  Gohda,  Y.;  Tsuneyuki,  S.   Anharmonic  force  constants  extracted  from  first-principles molecular dynamics: Applications to heat transfer simulations.Journal of Physics Condensed Matter 2014,26, 225402)

Round 2

Reviewer 2 Report

It can be accepted in this version.

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