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Dave Bacon is a theoretical ski bum who is also a pseudo 
Hm, today we seem to have a posting from beyond the grave, arXiv:1003.2133:
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
Authors: John von NeumannAbstract: It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
Physical Science
Comments
Well, sort of. The submitter is Roderich Tumulka, Assistant Professor: Department of Mathematics Rutgers University. He's written on QM, such as Bohmian mechanics. Here's the scoop, from http://www.math.rutgers.edu/~tumulka/papers :
English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
arXiv:1003.2133 [abstract, PS, PDF]
I'm happy to do some Google spade work for you Dave, I know you don't have time for it all. [Note to commenters: you must out-space colons etc. or they will include in the effective URL and spoil it. Nor can you get away with multiple URLs.]
BTW, is it really true that von Neumann made a fundamental math error in his work on QM, supposedly revealed by John Bell? More about it at http colon oolong.co.uk/causality.htm. Maybe, but I'll bet JvN would never have been suckered by that certain something my fans know I must be hinting at.
PS: Happy Pi Day! It's also Albert Einstein's 131st birthday. That's an interesting coincidence, not made much of it seems. Why not call it Einstein-Pi day etc?
Posted by: Neil B | March 14, 2010 4:27 PM
This is a very interesting post, Dave!
Especially interesting is von Neumann's explicit assumption that (in modern language) questions about ergodicity and the approach to thermodynamical equilibrium are all about symplectic (reversible) dynamical flow.
Nowadays, at molecular scales anyway, no one regards classical dynamics as being purely symplectic ... that's why there are roughly two articles about (classical) "thermostats" for every one article about (quantum) "Lindblad processes".
This is interesting because, aren't thermostats and Lindblad processes are really the *same* dynamical entity? ... so really we shouldn't be talking about "thermostatic" quantum systems instead of "open" quantum systems?
In which case, many powerful new tools become available from analyzing ergodic processes ... after all, what sense is there, in posing these questions in a way that makes them both mathematically harder *and* less physical?
Posted by: John Sidles | March 14, 2010 7:31 PM
I was supposed to coauthor with von Neumann's team-mate Stan Ulam, as confirmed by a public videolink via Bell Labs, but he died before we could get far along, other than his backing my work on decompositions of semigroups of differential operators of nonlinear ODEs in metabolisms of living cells.
Von Neumann wept on his deathbed that he'd wasted his later liufe, that he should have finished his cellular automata work with Ulam, reducing delta T to and spacial cell-size to zero and turning difference equations to continuous differential equations, and "solving the secret of life." Von Neumann felt that he alone had the right stuff to formulate and solve these equations.
Posted by: Jonathan Vos Post | March 15, 2010 2:27 AM