PONE-D-23-39285A Thermodynamic Definition and Equation of State for a Model of Political Election CyclesPLOS ONE

Dear Dr. Mantzaris,

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Mohammad Tariq

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: No

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The paper is concerned with the demonstration of the way a simulation of political discourse can utilize relationships between the variables affecting political engagement, and through those relations provide a correspondence between the variables of the social system and those of a thermodynamic system. The formulation proposed by the paper is significant concerning social physics to view social phenomena with physical principles.

Please kindly find below my recommendations to improve the paper:

The novelty of the paper can be stated more clearly.

The abstract can be revised to show the objective of the paper in a more evident way.

The distinctive parts of the paper can be stated so that the difference of this paper with previous ones can be shown.

I would also like to recommend English editing. For example, the first sentence in the abstract can be shortened or edited to make it clearer in meaning.

The authors can check if all the figures have been cited appropriately in the text.

Yours faithfully,

Reviewer #2: Review on manuscript:

„A Thermodynamic Definition and Equation of State for a Model of Political Election

Cycles”

--

The manuscript adresses new methodology for analysis of political elections processes. Political

election process relies on the metodology of classical statistical physics that is highly interlinked

with thermodynamics.

The concept of temperature is defined as dQ=dS/T so T=dS/dQ, where dQ stands for the transfered

heat or change of Hamitlonian energy. Such reasoning is not included in presented manuscript.

Therefore usage of term temperature is not fully justified.

The table with defined variables C(i,j,t)=C(x,y,t), M(i,j,t), I(i,j,t) shall be included for clarification

of manuscript. From the text we know that :

a) „A matrix is formed from the voting affiliation values, C, for each agent at their lattice positions

for each time point”,

b) „I is another matrix which holds the state of the ideological mismatch of an agent with their

locality”,

c) „ The matrix, M, contains the value for the voting action of each agent in the lattice at each time

point”.

Closer inspection of used quantities show certain similarity to Ising model and mean field theories.

Scalar field C is noting else equivalent to spin up or spin down in Ising model (with possible

accounting of fact that spin can have -3/2,-2/2,-1/2,0,1/2,2/2,3/2) etc.

The A shows effective local field (mean field) or its lack (as Superconducting Order Parameter or

Magnetization), while M accounts for possible gradient of me of I effective field.

In case of Ising model energy of a configuration σ is given by the Hamiltonian function

H(σ)=−∑〈 〉 i,j J(i,j)σiσj−μ∑j hjσj ,

where sums are over N by N lattice.

Therefore σi(x,y,t)is analogical to A(x,y,t) field, Step Function of (hi(x,y,t)) field is analogical to

M(i,j,t) field, while I(x,y,t) field is bit analogical to gradient of I(x,y,t) or momentum in quantum

mechanical terms. Coarse graing procedure is commonly known in statistical physics and can be

identified in Authors CMI model.

In such a way Hamiltonian for used „CMI” model (C(x,y,t), M(x,y,t), I(x,y,t)) shall be identified.

Then partition function denoted by Z shall be determined. Even Wikipedia gives broad description

of this metodology (https://en.wikipedia.org/wiki/Ising_model

https://farside.ph.utexas.edu/teaching/329/lectures/node110.html ,

https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics) ).

Equation of State is not fully justified. The manuscript cites:

T=exp(n_total), P=exp(n_pheripheral), V=exp(n_political), PV=T.

Therefore, manuscript implies operator equation: exp(n_pheripheral)exp(n_political)=exp(n_total).

How such operator equation can be justfied.

The Question is operator equation n_pheripheral+n_political=n_total.

If commutator [n_pheripheral,n_political] is equal to zero?

Schroedinger equation indeed is operator equation:

Ekinetic=[p^2/(2m)], Epot=V(x), Etotal=Ekinetic+Epot.

So if commutator [Ekinetic,Epot]=0 we can write

exp(Ekinetic)exp(Epot)=exp(Etotal) and nonzero commutator [Ekinetic,Epot] not equal 0, so

exp(Ekinetic+Epot)=exp(Etotal)

In Quantum Mechanics we have for example

H(t)|psi(x,t)>=i*hbar (d/dt)|psi(x,t)> leading to |psi(x,t)>=exp[(1/i*hbar)Int(H(t1),t0,t)]|psi(x,t0)>.

The title supposed to be changed into „A Possible Thermodynamic Definition and Equation of State

for a Model of Political Election Cycles”.

The manuscript shall cite additional positions:

P1) Van Kampen, „Stochastic Processes in Physics and Chemsistry”.

→ proper definition of temperature

P2) „Thermodynamics in Stochastic Conway’s Game of Life”

[ https://www.mdpi.com/2410-3896/8/2/47 ]→ methodology of thermodynamical description of

Game (as Election Process) is given with proper definition of temperature for given cellular

automata system.

P3) „Equivalence between finite state stochastic machine, non-dissipative and dissipative tight-

binding and Schrödinger model”(doi: 10.1016/j.matcom.2023.02.018 ) → methodology of mapping

Classical Statistical Physics Problem to Quantum Mechanics is Specified.

Major revision of article is required.

Temperature needs to be properly defined.

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Reviewer #1: No

Reviewer #2: No

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PONE-D-23-39285R1A Possible Thermodynamic Definition and Equation of State for a Model of Political Election CyclesPLOS ONE

Dear Dr. Mantzaris,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Apr 05 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Mohammad Tariq

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

==============================

      The manuscript is in good shape now. The authors need to address the comments of the reviewer #2.

==============================

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: I Don't Know

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The structure of the paper is well-organized. The paper is well-written with steps explained in good details. The novel aspects have been very duly explained as well. The recommendations have been integrated into the study which has been improved accordingly.

The paper can be considered suitable for publication.

Yours faithfully,

Reviewer #2: The improvements of manuscript has been conducted, but not fully in all suggested aspects.

The most troublesome is definition of temperature and thermodynamic cycle assigned to Model of Political

Election Cycles. Apriori Authors suggest the simplest equation of state pV=nRT as it is the case of ideal gas (as effectively describing political election cycle). Most gases or physical systems have much more complicated equation of state. Furthermore relation dS=dE/T or equivalently dE/dS=T is the best phenomenological definition of temperature T. Such definition is not undertaken in manuscript since Authors have not proposed any definition of Hamiltonian or energy in system of interacting agents in election cylce. One can report that definition of entropy was given in manuscript.

Due to this fact I recommend to add one sentence in conclusion section:

"Further justification of usage of thermodynamic cycles methodology in political election cycle shall be attempted with

introduction of definition of effective Hamiltonian (that is dependent on (C,M,I) ), so Hamiltonian change dE accompanied with entropy change dS will lead to temperature dependence expressed by formula T=dE/dS " .

Once this sentence in Conclusion section is added I recommend article for publication.

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If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: Yes: Yeliz Karaca

Reviewer #2: No

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A Possible Thermodynamic Definition and Equation of State for a Model of Political Election Cycles

PONE-D-23-39285R2

Dear Dr. Mantzaris,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Mohammad Tariq

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments: