Chris Aldrich

First, let's unpack your question a bit. What we're really doing is taking mathematical form, function, and theory and apply it in some sort of unifying manner to unify the areas of information theory and statistical thermodynamics.

You can also ask your question in the reverse direction to apply the mathematics of information to thermodynamics as well as there should be a mathematical duality of sorts, if in fact the two are directly related.

First, let's unpack your question a bit. What we're really doing is taking mathematical form, function, and theory and apply it in some sort of unifying manner to unify the areas of information theory and statistical mechanics and thermodynamics.

You can also ask your question in the reverse direction to apply the mathematics of information to thermodynamics as well as there should be a mathematical duality of sorts, if in fact the two are directly related.

The original link between the two areas stems from a paper by E.T. Jaynes entitled "Information Theory and Statistical Mechanics" (downloadable from http://bayes.wustl.edu/etj/articles/theory.1.pdf). Since then there has been a lot of uninformed back and forth in the literature from agreement to flat out denial, primarily as a result of the multitude of areas from which a researcher can approach the topics and rarely are many/any experts in more than one of these areas. (I specifically recall an article in 2011-2012 in the esteemed journal Science from a senior researcher in information theory that flatly stated there was no link between the two fields!)

Since then, in my opinion, the best source tying the fields together mathematically is A Farewell To Entropy: Statistical Thermodynamics Based on Information by Arieh Ben-Naim [http://www.amazon.com/gp/product/9812707077/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=9812707077&linkCode=as2&tag=itbio-20&linkId=WDUVNEIJG5BIO242]. In it he closely and coherently ties the two fields directly together and does a reasonable job of pointing out problems with some of the more popular misconceptions and conflicts in the literature. (For those without the physics, engineering, or math backgrounds in these subjects, I can also highly recommend Arieh Ben-Naim's forthcoming book Information, Entropy, Life and the Universe: What We Know and What We Do Not Know [http://www.amazon.com/gp/product/9814651672/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=9814651672&linkCode=as2&tag=itbio-20&linkId=WKTUT4I7WDIYS5MG] which is due out at the end of May.)

As for other connections, I've not seen anything as direct, primarily as there aren't any other major concepts with the exact same name. However, because of the underlying mathematics, I strongly suspect that there are many similar 'concepts'. A few in particular, I have a feeling will come out of the more rigorous mathematical frameworks based on Lieb and Yngvason’s concptualization of thermodynamics (see Resource Convertibility (Part 1)[https://johncarlosbaez.wordpress.com/2015/04/07/resource-convertibility-part-1/] and The Entropy Principle: Thermodynamics for the Unsatisfied: Andre Thess [http://www.amazon.com/gp/product/3642133487/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=3642133487&linkCode=as2&tag=itbio-20&linkId=3XLV4PT33UDZ2XLW].) Given the power of the mathematics and the more abstract nature of information theory, I suspect that thermodynamics and statistical mechanics will eventually be viewed as a sub-area or application of information theory.

Another fruitful area of conceptual similarities is slowly grown out of quantum information theory and the statistical mechanics of black holes, though there is some heavily rarified air surrounding these given the required background needed to operate with them both simultaneously.