Many Body in General Relativity: A Thermal Equivalence Principle
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript addresses an interesting and ambitious theme at the interface of general relativity, relativistic kinetic theory, and statistical mechanics. However, in its present form, I do not find that the central claim, namely the formulation of a “thermal equivalence principle”, is established with sufficient rigor. Much of the manuscript reads as a review of standard material, while the original contribution is concentrated in the final section and is not clearly separated from the review component.
My main concern is that the derivation of the central result is too formal and relies on assumptions and identifications that are not sufficiently justified. In particular, the transition from the averaged trace of Einstein’s equations to the introduction of a virial inverse temperature, and then to the statement \tilde T(x), appears to depend on definitions and normalization choices rather than on a general physical derivation. As a result, the conclusion that this establishes a new “thermal equivalence principle” is currently too strong.
The manuscript would benefit from a substantial revision of the introduction and literature review. The present version does not sufficiently position the work within the broader literature on relativistic thermodynamics, thermal equilibrium in curved spacetime, and statistical approaches to gravity. The citation pattern is also too heavily centered on the author’s own previous works.
I also recommend a major restructuring of the manuscript. The author should decide whether this is intended to be a review/perspective article or an original research paper. If it is a research paper, the standard review material should be shortened considerably and the novel derivation should be expanded, clarified, and tested more critically. If it is a review, then the manuscript should provide a broader and more balanced account of the literature.
Author Response
Dear Editor,
I would like to thank the Referees for their careful reading of the manuscript and for their comments/suggestions.
I copy below their reports and then I answer to their concerns explaining the changes made in the revised version which are marked in red color.
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Referee 1
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The manuscript addresses an interesting and ambitious theme at the interface of general relativity, relativistic kinetic theory, and statistical mechanics. However, in its present form, I do not find that the central claim, namely the formulation of a “thermal equivalence principle”, is established with sufficient rigor. Much of the manuscript reads as a review of standard material, while the original contribution is concentrated in the final section and is not clearly separated from the review component.
My main concern is that the derivation of the central result is too formal and relies on assumptions and identifications that are not sufficiently justified. In particular, the transition from the averaged trace of Einstein’s equations to the introduction of a virial inverse temperature, and then to the statement \tilde T(x)=T(x), appears to depend on definitions and normalization choices rather than on a general physical derivation. As a result, the conclusion that this establishes a new “thermal equivalence principle” is currently too strong.
The manuscript would benefit from a substantial revision of the introduction and literature review. The present version does not sufficiently position the work within the broader literature on relativistic thermodynamics, thermal equilibrium in curved spacetime, and statistical approaches to gravity. The citation pattern is also too heavily centered on the author’s own previous works.
I also recommend a major restructuring of the manuscript. The author should decide whether this is intended to be a review/perspective article or an original research paper. If it is a research paper, the standard review material should be shortened considerably and the novel derivation should be expanded, clarified, and tested more critically. If it is a review, then the manuscript should provide a broader and more balanced account of the literature.
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Referee 2
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The author reviews some of the main many body systems in the GR framework and concludes with an extension into thermal equivalence. While I find the subject is genuinely interesting, the presentation lacks some clarity and should be improved before publication. I have some concerns of the degree of the actual new content added to this contribution, as I mention below.
Apart I have some other issues that should be solved. Some parts of the text appear in red, from previous edits I assume. However, having a section with a single statement is odd. It should be accordingly explained for the general reader. On page 10 some explanations appear as foot notes so it is annoying to read and lack sufficient space to describe the fact (see the long note 7). Pages 11 and 12 are by far the most interesting part but they lack physical link to other systems. The authors could perhaps comment on stellar systems where this principle could indeed have interesting consequences. To do so, they can rely on pioneering treatments of free Fermi gases, for example.
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My Reply to Referee 1
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I thank the Referee for giving me the opportunity to improve the manuscript.
In an attempt to satisfy the Referee desire of a more structured paper I included a description of its organization at the end of the introduction and I created another section division between the introduction and the description of the stress energy tensor for free particles that was previously introduced in medias res.
I rephrased some parts of the introduction and I added references to some broader literature on relativistic thermodynamics, thermal equilibrium in curved spacetime, and statistical approaches to gravity for what concerns the construction of more accurate equations of state of a star. I did this when describing our novel equivalence principle in Section V. I also reduced self citations.
Regarding the main result of the work: the equivalence principle, I think that it is nice to see how the statistical physics theory and the general relativity theory can be made to be consistent one with the other. Even if this fact can be considered superfluous in my opinion it cannot be given for granted or even treated carelessly and it is certainly not trivial. I could not find it stated clearly anywhere in the literature of either general relativity or statistical physics. It issues a bridge between the two communities.
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My Reply to Referee 2
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I thank the Referee for giving me the chance of improving the manuscript. Accordingly I have extended the section with a single statement reporting the results from Ref. [2]: [R. Fantoni, White-dwarf equation of state and structure: the effect of temperature, J. Stat. Mech. , 113101 (2017)].
I have removed Footnote 3 and included it in the main text but left untouched Footnote 7 since I regard the definition of the index of a vector field as something that either the reader already knows or if this is not the case than he may benefit of the note. But being it just a mathematical definition I do not regard necessary to include it in the main text so to avoid unecessary fragmentation of the flow of the discussion.
I added some physical links on page 13 as requested by the Referee regarding the importance of our equivalence principle when devising a more accurate equation of state for a star.
I hope that the revised version of the manuscript is suitable for publication in Quantum Reports Journal,
Best regards,
Riccardo Fantoni
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author reviews some of the main many body systems in the GR framework and concludes with an extension into thermal equivalence. While I find the subject is genuinely interesting, the presentation lacks some clarity and should be improved before publication. I have some concerns of the degree of the actual new content added to this contribution, as I mention below.
Apart I have some other issues that should be solved. Some parts of the text appear in red, from previous edits I assume. However, having a section with a single statement is odd. It should be accordingly explained for the general reader. On page 10 some explanations appear as foot notes so it is annoying to read and lack sufficient space to describe the fact (see the long note 7). Pages 11 and 12 are by far the most interesting part but they lack physical link to other systems. The authors could perhaps comment on stellar systems where this principle could indeed have interesting consequences. To do so, they can rely on pioneering treatments of free Fermi gases, for example.
Author Response
Dear Editor,
I would like to thank the Referees for their careful reading of the manuscript and for their comments/suggestions.
I copy below their reports and then I answer to their concerns explaining the changes made in the revised version which are marked in red color.
------------------------------------------------------------------------------------
Referee 1
------------------------------------------------------------------------------------
The manuscript addresses an interesting and ambitious theme at the interface of general relativity, relativistic kinetic theory, and statistical mechanics. However, in its present form, I do not find that the central claim, namely the formulation of a “thermal equivalence principle”, is established with sufficient rigor. Much of the manuscript reads as a review of standard material, while the original contribution is concentrated in the final section and is not clearly separated from the review component.
My main concern is that the derivation of the central result is too formal and relies on assumptions and identifications that are not sufficiently justified. In particular, the transition from the averaged trace of Einstein’s equations to the introduction of a virial inverse temperature, and then to the statement \tilde T(x)=T(x), appears to depend on definitions and normalization choices rather than on a general physical derivation. As a result, the conclusion that this establishes a new “thermal equivalence principle” is currently too strong.
The manuscript would benefit from a substantial revision of the introduction and literature review. The present version does not sufficiently position the work within the broader literature on relativistic thermodynamics, thermal equilibrium in curved spacetime, and statistical approaches to gravity. The citation pattern is also too heavily centered on the author’s own previous works.
I also recommend a major restructuring of the manuscript. The author should decide whether this is intended to be a review/perspective article or an original research paper. If it is a research paper, the standard review material should be shortened considerably and the novel derivation should be expanded, clarified, and tested more critically. If it is a review, then the manuscript should provide a broader and more balanced account of the literature.
------------------------------------------------------------------------------------
Referee 2
------------------------------------------------------------------------------------
The author reviews some of the main many body systems in the GR framework and concludes with an extension into thermal equivalence. While I find the subject is genuinely interesting, the presentation lacks some clarity and should be improved before publication. I have some concerns of the degree of the actual new content added to this contribution, as I mention below.
Apart I have some other issues that should be solved. Some parts of the text appear in red, from previous edits I assume. However, having a section with a single statement is odd. It should be accordingly explained for the general reader. On page 10 some explanations appear as foot notes so it is annoying to read and lack sufficient space to describe the fact (see the long note 7). Pages 11 and 12 are by far the most interesting part but they lack physical link to other systems. The authors could perhaps comment on stellar systems where this principle could indeed have interesting consequences. To do so, they can rely on pioneering treatments of free Fermi gases, for example.
------------------------------------------------------------------------------------
My Reply to Referee 1
------------------------------------------------------------------------------------
I thank the Referee for giving me the opportunity to improve the manuscript.
In an attempt to satisfy the Referee desire of a more structured paper I included a description of its organization at the end of the introduction and I created another section division between the introduction and the description of the stress energy tensor for free particles that was previously introduced in medias res.
I rephrased some parts of the introduction and I added references to some broader literature on relativistic thermodynamics, thermal equilibrium in curved spacetime, and statistical approaches to gravity for what concerns the construction of more accurate equations of state of a star. I did this when describing our novel equivalence principle in Section V. I also reduced self citations.
Regarding the main result of the work: the equivalence principle, I think that it is nice to see how the statistical physics theory and the general relativity theory can be made to be consistent one with the other. Even if this fact can be considered superfluous in my opinion it cannot be given for granted or even treated carelessly and it is certainly not trivial. I could not find it stated clearly anywhere in the literature of either general relativity or statistical physics. It issues a bridge between the two communities.
------------------------------------------------------------------------------------
My Reply to Referee 2
------------------------------------------------------------------------------------
I thank the Referee for giving me the chance of improving the manuscript. Accordingly I have extended the section with a single statement reporting the results from Ref. [2]: [R. Fantoni, White-dwarf equation of state and structure: the effect of temperature, J. Stat. Mech. , 113101 (2017)].
I have removed Footnote 3 and included it in the main text but left untouched Footnote 7 since I regard the definition of the index of a vector field as something that either the reader already knows or if this is not the case than he may benefit of the note. But being it just a mathematical definition I do not regard necessary to include it in the main text so to avoid unecessary fragmentation of the flow of the discussion.
I added some physical links on page 13 as requested by the Referee regarding the importance of our equivalence principle when devising a more accurate equation of state for a star.
I hope that the revised version of the manuscript is suitable for publication in Quantum Reports Journal,
Best regards,
Riccardo Fantoni
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI accept in present form
