Well, under a rather confusing set of circumstances, my second law paper was rejected by PRA – a second time (even though I hadn’t yet made any changes and didn’t realize I had ‘resubmitted’). In any case, I’ll be taking up Terry Rudolph up on his offer of assistance for the next re-write – and that will put the number of people assisting and/or commenting on this over the past few years into the double-digits, I think.
Anyway, my point isn’t to gripe again about the rejection, per sé. Rather, I wonder if the basic idea even has a hope of getting published at all. I know Terry thinks the fact that I derived the Cerf-Adami inequalities without reference to Markov processes is important enough to publish and I’ll certainly re-write the paper to focus on that. But, the primary idea that I have been trying to get across is that the CF inequalities are a statement of the second law of thermodynamics, and therein lies the problem – no one seems to agree on what that law is! And, yet, we continue to teach it to students as if we know it.
Consider some remarks from the first reviewer as well as those from a second reviewer they brought in to validate the first. These should make it clear that physicists either have no idea what the second law truly is or simply can’t agree on it’s statement (which was partially the point of my paper).
“The second law of thermodynamics is much more that ‘just a strong statement on the behavior of probabilities’. This assertion in the introduction, even if found in ref.7, is so upsetting for many scientists, that could stop a good number of them at the out set, as it appears to be the case for the previous referee.”
Comment: This is an old idea (e.g. Eddington held this view) that still has a strong following (e.g. my Ref. 7 is to Dan Schroeder’s book and Schroeder knows enough to have also co-authored one of the definitive texts on quantum field theory). Clearly I should have added a statement indicating I was using this ‘interpretation,’ but it is an interpretation that is commonly taught. So, if it’s wrong, why do we teach it? And, my entire point is that there is a problem with the second law of thermodynamics which this reviewer seems to validate by pointing out that “[w]hat I am trying to say is the second law of thermodynamics has been discussed and is being discussed by many, in various fields of science and engineering, and if it were only what the author says (or rather hints to), namely some inequality about probabilities, it would be quite strange that we are still here discussing it well over a century after its first statement.” Then why, I repeat, does it still appear in published work by well-known and respected authors?
“In the conclusions the author writes that ‘our definition of entropy needs altering,’ but this is nonsense, because we should not be surprised to see problems if a classical concept (Shannon entropy) is used to describe quantum dynamics. All we need to do (to remove inconsistencies) is to use von Neumann entropies instead. The point you are raising was made by Brukner, who is acknowledged for discussions, so I find it hard to believe that this is a coincidence. But be that as it may, It is still nonsense to say that Shannon entropy needs to be amended. One should just stop using it in the quantum regime. The 2nd law is perfectly well described with conditional quantum entropies, as Cerf and Adami have in fact shown.”
Comment: OK, here I really think the reviewer lets his personal views cloud his judgement. First, if classical and quantum entropies truly do not describe the same (or at least related) phenomena, then don’t use the same freakin’ word to describe them. Second, Caslav ain’t the only one who sees/saw a serious problem with the notion of entropy in general. Carnap wrote a whole treatise on it (that was edited by Abner Shimony who is the ‘S’ in the CHSH inequalities, by the way, but perhaps philosophers can’t be taken that seriously)! Third, how can one so blithely gloss over the quantum/classical dichotomy? Somewhere they have to be reconciled with one another since they both describe the universe on different levels, and, at some point, there is a crossing from one into the other. Fourth, von Neumann entropies can reduce to Boltzmann-Gibbs-Shannon entropies! Therefore, they have to be related! (See, for example, Sakurai on this topic.)
“I know perfectly well what degree you have and what you teach. It is still not true that the ‘fundamental assumption of statistical mechanics is all accessible microstates are equally probable in the long run’. It is not true, and perhaps you should go back and reread a stat. mech. textbook. Again: “microcanonical vs. macrocanonical.”
Comment: Perhaps I should have directly quoted the multiple stat. mech. texts that say these exact words. The comment was in response to a comment I made in my reply (which I didn’t realize was taken as a reply – I was only asking for clarification on some points) in which I made it clear that I know statistical mechanics pretty well. In fact, I know it better than I know a lot of other subjects since I am a former mechanical engineer who cut his teeth on thermo-fluid problems. This is aside from the fact that I have been teaching it regularly for almost six years.
In any case, this makes me wonder if a convincing argument concerning the second law is even possible regardless of what it is related to, since it seems that no one can agree on what the second law is! Perhaps Landau and Lifshitz did the smart thing by calling it the ‘law of entropy increase.’ In any case, this basic idea – that the CF inequalities are another statement of the second law (or a version of it, anyway) – seems so obvious to me that I am utterly blown away at the fact that, in two years, I have not yet found anyone who really believes in what I’m trying to do (even Barry admitted to being somewhat agnostic on the topic) except, perhaps, Ken Wharton, but no one believed in Ken’s work either until recently (he’s still having a rough go of it despite his work garnering him an invitation to spend a week at the Perimeter Institute).