Thermodynamics and Nonlocality in Continuum Physics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Regarding the statement in lines 14 and 15, the reviewer holds a different opinion than the authors':

If we assume that the behavior at a material point is affected by its neighborhood, then space nonlocality must be considered in the modeling of the material.

Regarding time nonlocality if we assume that the material is not viscoelastic then its past history plays no role. In case of plasticity and viscoplasticity we consider "weak non locality" by the rate equations of strain and internal variables.

2. In lines 31 and 32, give the reference (5) correctly by stating both authors' names in the order appearing in the paper.

3. In Eq. (1) what is the meaning of 'power density' ω ?

4. a. In line 42 and Eq. (3) the symbols for hyperstress σ differ. Please, make the correction.

b. In lines 36 and 42 the concept of hyperstress is introduced. 

It will be very helpful for the reader an explanation of the concept to be provided, why it is needed and maybe an appropriate reference.

5. Lines 141 to 143 "The difference among the schemes...." are not clear.

Do the authors mean "representing the displacement gradient" instead of the strain gradient?

6. Line 245: (31) is an equality not an inequality.

 

7.  Line 400. Please, cite the correct references. They are not Coleman et al.

 

8.  Line 512:  The relation following this line is not an inequality, but an equality.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article delves into the crucial area of thermodynamics and non-locality in continuum physics. It does so by employing constitutive functions that are dependent on certain gradients, thereby adhering to the second law of thermodynamics and balance equations. The specific focus is on elastic solids, heat conductors, and magnetic solids, all of which are of significant interest in the field.

 

This study can make valuable and relevant scientific contributions to the broader scientific community. The manuscript is not just well written, but it also presents the scientific contributions in a comprehensive manner, ensuring a thorough understanding. Some case studies applications could have further improved the conclusions. However, I will support the publication of this research paper in the current form.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. the introduction the focus on nonlocality in elasticity, heat conduction, and magnetism, it would be helpful to do remark in precise form statement of the paper’s specific objectives or hypotheses. So would allow readers to better understand the intended contributions relative to existing theories.
2. The paper cointains a lot detailed mathematical development and extensive,  but the could be more atractive from a more explicit interpretation of the physical implications of the obtained equations. 
   
   
3. the authors might consider integrating additional references from recent years (2022–2025) that address applications of nonlocal thermodynamics or gradient theories in emerging materials, such as metamaterials, nanostructures, or magnetic composites.
   
   

Author Response

Please see the attachment.

Author Response File: Author Response.pdf