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Papers on Entropy in Quantum Mechanics Framework

  • #1
VVS
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Main Question or Discussion Point

Hey,
I am going to write my bachelor's thesis on Entropy in a Quantum Mechanical Framework. My professor told me he would refer me to some literature. However it will take him some time.
I would like to get started myself. Could you please refer me to papers, books, articles? I have already read Shannon's paper on A Mathematical Theory of Communication.

Thank you
 

Answers and Replies

  • #3
Stephen Tashi
Science Advisor
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I don't know whether this article is available online to the general public.
http://scitation.aip.org/content/aapt/journal/ajp/57/11/10.1119/1.15810

I haven't kept up with the Fisher-information line of thinking since that article came out. This book review indicates Roy Freiden had more to say: http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/physics-from-fisher-info/ [Broken] Nowadays, you can find many hits on Fisher information and physics.
 
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  • #4
chiro
Science Advisor
4,790
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There is a book that looks at physics entirely from the point of Fisher Information which is very similar to entropy (it's basically the concept of information in statistics and is seen in the information matrix along with all of the statistical results in statistical inference).

The book is called "Physics from Fisher Information - A Unification" by B Roy Frieden published by Cambridge University Press.
 
  • #5
StatGuy2000
Education Advisor
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There is a book that looks at physics entirely from the point of Fisher Information which is very similar to entropy (it's basically the concept of information in statistics and is seen in the information matrix along with all of the statistical results in statistical inference).

The book is called "Physics from Fisher Information - A Unification" by B Roy Frieden published by Cambridge University Press.
The links that Stephen Tashi provided above include a review by Cosma Shalizi, (a physicist-turned-statistician and a professor at CMU, who writes a blog on various areas of science called the Three-Toed Sloth) who gave a negative review of the book by Frieden, and essentially state that much of the effort to look at physics entirely from Fisher information is misguided at best.

To the OP: Shalizi has provided links to numerous references that relate directly to the role of entropy in quantum mechanics. I've attached the links below.

http://bactra.org/notebooks/information-theory.html

http://bactra.org/notebooks/quantum-mechanics.html
 
  • #6
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Also take a look at eigenstate thermalization hypothesis (ETH). It's a tricky assumption quite crucial in quantum statistical mechanics, the analogue of the classical idea that the microcanonical and canonical ensemble are the same, which means--more physically speaking--that isolated systems or systems in contact with a thermal reservoir give similar results. In the classical case one can argue this quite convincingly, but I think that in QM it's quite mysterious, and probably not true in general.
 

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