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Your opening reminded me a bit of the motivating chapter of Andre Thess's book <a href="">The Entropy Principle (Springer, 2011)</a> in which he uses the fable of Hans who manages to waste away a block of gold until he has nothing.

The book was an interesting textbook-like conceptualization of Lieb and Yngvason's work, which I always thought was due for a more thorough mathematical framework. I'm glad to see you not only reference them, but you appear to do what I've always wanted. Can't wait to delve further into your actual paper.