QM and Crook's Fluctuation Theorem

[Jimster41]

Is there a bridge from QM to Crook's Fluctuation Theorem and/or the Jarzynski Equality?

More ambiguously, but maybe more directly, Is there thought to be a relationship between the QM-entanglement/decoherence/interference, and the SLOT?

I am worried I may be missing a discussion of this, due to lack of understanding of terms.

 

[atyy]

What is SLOT?

 

[Jimster41]

Second Law of Thermodynamics.

I got that acronym from somewhere on this forum. A lot less typing obviously.

Gotta put my electronic device into airplane mode for a few hours...

 

[atyy]

I might be wrong, but I believe the answer is "no". IIRC Crook's and Jarzynski's assume heat baths, so in a sense the quantum mechanics is already not pure. (Again, I am not terribly sure of this.)

However, there is work on getting from pure QM to the second law of thermodynamics - going back all the way to guess who - von Neumann! Yes, he was a great guy and thought about physics very physically, thinking hidden variables important enough to explore, even if he made a mistake in interpreting his theorem. Here are some recent papers that will point the way to the literature.

http://arxiv.org/abs/1007.3957
Strong and weak thermalization of infinite non-integrable quantum systems
Mari Carmen Bañuls, J. Ignacio Cirac, Matthew B. Hastings

http://arxiv.org/abs/1506.07494
Thermal equilibrium of a macroscopic quantum system in a pure state
Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka

http://arxiv.org/abs/1507.06479
Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
Hal Tasaki

http://arxiv.org/abs/1507.00262
Generalization of von Neumann's Approach to Thermalization
Peter Reimann

 

[Jimster41]

I tried to just get a feel for what question those papers were asking. If I understand correctly they were all trying to imagine what thermal dissipation looks like in the evolution of an unobserved many body QM system, given some Hamiltonian. Very interesting. So cool that in the first paper a numerical simulation of that process seems to go rogue!

I was more interested whether the boundary information proposed in @Demystifier's onion-like AdS/CFT model, which is how I had been picturing it (roughly of course) could be envisioned as a heat bath (information has temperature right) doing work on our bulk - via an analog of Crook's Probability Work theorem. Smolin's recent "maximal variety" paper seems to fit somehow, right in there,

 

[atyy]

In the usual AdS/CFT picture, a thermal state is a black hole, so thermalization is black hole formation.

http://arxiv.org/abs/hep-th/9912209
Black Hole Formation in AdS and Thermalization on the Boundary
Ulf H. Danielsson, Esko Keski-Vakkuri, Martin Kruczenski

http://arxiv.org/abs/1103.2683
Holographic Thermalization
Vijay Balasubramanian, Alice Bernamonti, Jan de Boer, Neil B. Copland, Ben Craps, Esko Keski-Vakkuri, Berndt Müller, Andreas Schäfer, Masaki Shigemori, Wieland Staessens

 

[Jimster41]

Found this in an old thread. Exactly the angle I was trying to get at.

http://arxiv.org/abs/quant-ph/0605031
Irreversibility in Collapse-Free Quantum Dynamics and the Second Law of Thermodynamics
M. B. Weissman
(Submitted on 2 May 2006)
Proposals to solve the problems of quantum measurement via non-linear CPT-violating modifications of quantum dynamics are argued to provide a possible fundamental explanation for the irreversibility of statistical mechanics as well. The argument is expressed in terms of collapse-free accounts. The reverse picture, in which statistical irreversibility generates quantum irreversibility, is argued to be less satisfactory because it leaves the Born probability rule unexplained.