Analogies between temperature and time in thermodynamics

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Looking through the book of abstracts for «XXI International Conference on Chemical Thermodynamics in Russia (RCCT-2017)» I came across the abstract of talk given by Peter Atkins (University of Oxford) titled «Thoughts about thermodynamics» (you'll find the whole abstract at the end of the post). One sentence of this abstract puzzled me; it was «There are fascinating analogies, such as those between temperature and time that might reveal deep truths about the fabric of reality.» I have reminiscences of having seen remarks about the mentioned «analogies» before (I can't remember where though).

Anyway, Atkins is a heavyweight in the field of chemical thermodynamics and his words should be taken seriously. Do you have any idea what those analogies between temperature and time are (especially in context of thermodynamics)?

The text of the abstract:
Elementary thermodynamics is so well established that there is perhaps little to discover and even less to consider when instructing our students. But is that really true? In this lecture I shall explore aspects of thermodynamics that remain interesting and which open up deep questions about this mature subject and which could lie in the back of our minds when teaching our students. There are deep questions to explore, such as why the laws of thermodynamics are valid. Why, for instance, is energy conserved? Why does entropy increase? There are fascinating analogies, such as those between temperature and time that might reveal deep truths about the fabric of reality. What happens when systems of interest are so small that fluctuations dominate the most probable values? What are the origins of the fundamental constants that characterize thermodynamics, such as Boltzmann’s constant and the gas constant? Did the originators of thermodynamics introduce unnecessary complications when formulating, for instance, the concept and measurement of temperature? What are the thermodynamic properties of the electromagnetic field: how is the Sun capable of driving processes on Earth? I shall explore these thoughts: they do not really open up revisions of elementary thermodynamics, but show that by reflecting on elementary principles, deep questions arise and can stimulate how we teach and encourage our students to become questioning scientists.​
 

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Andy Resnick
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Do you have any idea what those analogies between temperature and time are (especially in context of thermodynamics)?
Ryogo Kubo, in the early 1950s, noticed that the quantum mechanical partition function (used for many-body problems) could be regarded as a time-evolution operator in "imaginary time". That is, finite-temperature many-body physics problems can be reformulated in terms of a 'zero-temperature' imaginary-time problem. This approach he been developed over the decades and applied to a variety of problems (electron-phonon interactions, fluctuation-dissipation and linear response theories).

Now, a caveat: statistical mechanics is not a proxy for thermodynamics; statistical mechanics can be considered a microscopic foundation for thermostatics and possibly for thermokinetics. Regarding the abstract, I disagree that elementary thermodynamics has little to discover: indeed, there remain considerable open questions, ranging from the general (such as, when 'temperature' exists) to the more specific (such as, is the contact angle a thermodynamic quantity?)

Does that help?
 
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Does that help?
It surely is. Thank you!
This approach he been developed over the decades and applied to a variety of problems
I would appreciate you providing me with specific reference to a monograph or a review of applications of Kubo's idea (if you have such a reference at the ready, of course)? My guess is you refer to the so-called «Thermal field theory» (https://en.wikipedia.org/wiki/Thermal_quantum_field_theory). However, it seems weird to me that Kubo's name is not even mentioned in that article. So is there any chance you are referring to something else?
Regarding the abstract, I disagree that elementary thermodynamics has little to discover
Reading the abstract I got an impression that the first sentence was written for the sole purpose of underlining author's disagreement with this view.
 
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Andy Resnick
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It surely is. Thank you!

I would appreciate you providing me with specific reference to a monograph or a review of applications of Kubo's idea (if you have such a reference at the ready, of course)? My guess is you refer to the so-called «Thermal field theory» (https://en.wikipedia.org/wiki/Thermal_quantum_field_theory). However, it seems weird to me that Kubo's name is not even mentioned in that article. So is there any chance you are referring to something else?
My reference was Coleman's book:

https://www.cambridge.org/core/books/introduction-to-many-body-physics/B7598FC1FCEE0285F5EC767E835854C8

A few online documents I found that may be of interest:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0ahUKEwimmteg6IjcAhWC64MKHQVCBqAQFghTMAM&url=https://www.mrc-lmb.cam.ac.uk/genomes/madanm/balaji/kubo.pdf&usg=AOvVaw2h-_VkfTEAW-ojiI-GbbYb
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwimmteg6IjcAhWC64MKHQVCBqAQFgg1MAE&url=http://eduardo.physics.illinois.edu/phys582/LRT.pdf&usg=AOvVaw0zuFsPGQVLtsD6ulbdHMkI
 
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That pretty much answers my question. Thank you!
 

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