Bob Lloyd, professor emeritus of chemistry at Trinity College Dublin, wrote an opinion article in Mathematical Intelligencer (MI) commenting on Sewell’s not-quite-published AML article. This was mentioned in a previous thread, where Bob briefly commented. Granville was invited to participate but never showed up.
In response to Lloyd, Sewell submitted a letter to the editor. On advice of a referee, his letter was rejected. (Rightly so, in my view. More on that later.) Sewell has now written a post on Discovery Institute’s blog describing his latest misfortune. The post contains Sewell’s unpublished letter and some of the referee’s comments. I invite you to continue the technical discussion of Sewell’s points started earlier.
Sewell’s reply to Lloyd deals mostly with “X-entropies:”
Lloyd cites my example, given in my letter to the editor in a 2001 Mathematical Intelligencer issue, of carbon and heat diffusing independently of each other in a solid… He proceeds to show that these “entropies” are not independent of each other in certain experiments in liquids. This seems to be his primary criticism of my writings on this topic. I may have left the impression in my 2001 letter that I believed these different “X-entropies” were always independent of each other, but in the more recent AML paper, I wrote:
He then quotes from his AML paper and rambles on for another eleventeen paragraphs. Read at your own risk.
Here is my brief take on this. I will expand on it in the comments.
“X-entropies” are not new quantities. Sewell does not define them in any of his papers and blog posts, but my reading is that they are either other thermodynamic variables (e.g., chemical potential or pressure) or they are regular thermal entropies of different parts of a large system (configurational entropy of carbon and entropy of lattice vibrations in Sewell’s example). Either way, the 2nd law is not threatened. In the latter case, if the two subsystems can interact and exchange energy then the entropy in one can decrease; the decrease is amply compensated, and then some, by an increase of entropy in the other subsystem. We saw this in the previous thread with an ice cube in a glass of water and with spins in a ferromagnet. Compensation works. Sewell has no leg to stand on.