From the public discussion it appears that you have been able to successfully address all the points raised by the reviewers, and can only but encourage you to submit the revised version which I will review before acceptance.

Dear authors,

Thank you for having taken so much care in preparing your manuscript. It saved me a lot of work. Here are a few suggestions that you can implement at the proof level if you find them relevant.

- p. 2 l. 22 : temperatures can't be colder; they can just be lower !
- p. 5, l. 16: ... of molecule that describeS heat or thermal energy
- p. 5 l. 16 : ... "is absorbed and heats air and water (adds thermal energy)" (or at least reformulate the sentence such that the transitive character of the 'heat' verb is respected.
- p. 10, l 11: "first-order description". As far as I am concerned I like to reserve the phrase 'first-order' when it actually means that it is mathematically correct to first order. Perhaps "schematic". I leave it to you, though.
- p. 11 l. 19 : "empirical tuning" sounds like a pleonasm to me. Just "tuning"
- p. 11, l. 22 : "to be able to derive" : just write "to derive"

A last thing: punctuation is absent from formulae (i.e., no point, comma, etc. after equations). Some mathematicians insist to have punctuation, and I tend to agree. However, the editor in chief has the last word !