Entropy Production Assumption and Objectivity in Continuum Physics Modelling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper provides  an interesting formulation of thermodynamically consistent models. In particular, a generalized form of the second law of thermodynamics is proposed, in which  entropy production is treated as  a constitutive function independent of the other constitutive functions. Particularly illuminating is the discussion, in the context of deformable dielectrics, of the consequences of considering entropy production as a constitutive function rather than deriving it from the Clausius-Duhem inequality, as well as the analysis of the restrictions imposed by the principle of objectivity. The paper is scientifically sound, and in my opinion, it is ready for publication.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The paper by A. Morro titled Entropy production assumption and objectivity in the modelling of continuum physics is full of rational-thermodynamics and mechanics-based formal calculations, being less transparent than a concrete demonstration based on examples. The present reviewer thinks that papers 10 and 14 by the current author contain enough essence of what the author wished to pass to the readers, and therefore, an appreciable novelty is not seen in the underlying study, or it is not delineated enough by the author. Moreover, the current reviewer has a serious problem with a typically rational-thermodynamics statement: "the second law of thermodynamics is considered in a generalized form where the entropy
production is given by a constitutive function, possibly independent of the other constitutive functions." This is repeated twice in the Abstract and the Conclusions. It is because in Onsager-Prigogine type thermodynamics, entropy production is not mixed up with constitutive relations (or, some functions), and in equilibrium Boltzmann-Gibbs thermodynamics, the entropy production ought to be set to zero since the entropy maximum principle prevails. Next, as for the application to the materials such as deformable dielectrics, for which the symmetric and asymmetric tensorial parts are of importance, the notation is not well-explained to a potential reader, which looks as a methodological shortage here ("skw", "sym", etc.). Last but not least, a comment on employing the rational thermodynamics methodology (as also developed in papers and books by I. Miller and others) could elucidate certain too-formal pieces of the text, especially those pointing to the entropy production principles in matter-aggregating (mesoscopic) systems. 

To recap, all the drawbacks listed above as well as the continuum mechanics-oriented literature, have to be changed not too extensively but accordingly. Also, the presented formalism can yield at least one lucid and convincing (simple) example that it works based on a specific system.  As a consequence, the current referee does propose a major revision to the paper's contents. (Certain illustrative graphics may help uncover the paper's merits, too.)  

And finally,  a remark is passed to the Authors that when speaking about the principles of continuum physics, the proportions with respect to continuum-mechanics literature can be changed, especially those concerning the meaning and significance of entropy production (see a feature paper by D. Reguera et al. titled The Mesoscopic Dynamics of Thermodynamic Systems https://pubs.acs.org/doi/10.1021/jp052904i or that of Physica A 373, 43-57 titled Kinetic–thermodynamic effects accompanying model
protein-like aggregation: The wave-like limit and beyond it https://www.sciencedirect.com/science/article/abs/pii/S037843710600642X?via%3Dihub, as some obvious but two examples. 

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript's summary is very consistent with the overall focus of the work, clearly presenting the ideas and points covered.

The writing is easy to follow, well-structured, and presents a novel approach that may be of interest to science and engineering.

Although the work is of a high standard, it is easy to follow due to the author's clear writing.

I would just like to suggest that the author add two more current references to the manuscript.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

Entropy production is discussed in the framework of continuum mechanics, having in mind the constraints of angular momentum and of objectivity. The discussion, which is quite general per se, is applied to dielectrics. The topic is discussed in a systematic way. There are some typos, listed below. However, in my opinion there is also a major fault, which needs correction.

The author stresses the generality of his results. However, there is an ansatz - namely, equation 37 - which both equations 38 and 39 and (partially at least) and the following discussion rely upon. Physically, the ansatz means that the contribution of the quantity γ is split in two separate contributions, namely of the quantities γ_Q and γ_D. The Second Principle requires that both γ_Q and γ_D are non-negative. 

However, the physical meaning of the quantities γ_Q and γ_D are discussed nowhere throughout the paper. This puts a strong limit on the relevance of the whole discussion to real-life physical systems.

In particular, I have not been able to find any information concerning γ_D. 

As for γ_Q, equation 37 seems to be justified because in Sec. 5.4 its consequence, equation 39, leads in turn to the well-known Maxwell-Cattaneo law (which is even relativistically invariant) at least if ν = 0. But once more: what does 'ν = 0' mean? Under which physical conditions does this assumption apply?

Remarkably, the reader finds the following words at the beginning of Sec. 5.4: 

'this model shows that g need not coincide with, or merely be proportional to, the pertinent entropy production γ.'

(I suppose this gamma is just γ_q) here, according to Sec. 5.2, 'g is the entropy production to be determined'. However, the only explicit expression for γ_q provided in the paper is found just before the beginning of Sec. 6. Here, γ_q is proportional to the familiar entropy production to heat conduction whenever Fourier's law holds, i.e. in the case where both ν and α vanish. 

Lack of general expressions for γ_D and γ_Q - and, more generally, lack of physical justification of the ansatz equation 37 - hampers the relevance of the whole discussion. 

I wholeheartedly agree that the attempt to find information concerning the entropy production with the only help of objectivity and conservation of angular momentum deserves careful attention. However, I find really confusing this superposition of intertwined general results and tacit assumptions, a superposition all the more confusing because of the quite abstract nature of the discussion. 

I strongly recommend that the author rewrites the paper, with a list of the main assumptions just at the beginning. Should it be impossibile to list all of them at the beginning of the paper, they could be better highlighted at the beginning of the Sections they are invoked for the first time. 

After such revision, I find that the paper surely deserves publication.

As for the typos:

- in Sec. 4, just after equation 22: the sentence 'only if a dependence
of k on a vector and this is not the case.' is uncomprehensible. Some words are cleaarly missing.

- in Sec. 10, the line 'Objectivity principle' should be somehow stressed - e.g. in bold italics - for better reader's comprehension

- In the line just after eq. 35: what does the '??' stand for?

- The symbols J and W are introduced in equation 27 and Sec. 5.4 respectively. Their meaning is likely to be obvious to specialists in continuum mechanics; however, it should be better briefly explained to the general reader. 

Author Response

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Reviewer 5 Report

Comments and Suggestions for Authors

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Comments for author File: Comments.pdf

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The Author has made a substantial progress in improving paper's quality. Especially, he established formally unique connection between the entropy production in NET and RT, by considering the inner product of diffusion flux and gradient of the chemical potential, which is an interesting extension of the previous version - it has been made according to the referee's suggetion, and it is well-done. He also has provided a two-component fluid mixture example (the only minor drawback is that no illustrative graphics have been added for encouraging some more readers to read the paper). Moreover, the proportion of cited literature, interpenetrating between 'physics' and 'mechanics' customary addressed points of view, has been properly changed. Other minor, mostly notational points, have been addressed with a proper scrutiny, too. 

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

In the present version, the paper is highly readable. Really, I enjoyed it! Just one minor correction, for the sake of better clarity. Just after equation (27) (where - as far as I can see - the symbol J occurs for the first time) and before the words 'upon a direct calculus we find that', I find the computation of a derivative which clearly shows that J is a Jacobian. As obvious as it may seem, the statement 'J is a Jacobian' is written nowhere in the paper. As for a reader which is not familiar with the formalism of continuum mechanics, this can be confusing. Given the considerable effort of the author in explaining all other things in detail, I would like to suggest that a (short!) explanation of the meaning of the symbol 'J' is added to the paper before publication. 

Author Response

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