What are some good resources for learning about information theory?

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Discussion Overview

The discussion revolves around resources for learning about information theory, particularly its applications and connections to physics and statistical mechanics. Participants express interest in both introductory materials and more advanced texts that relate information theory to physical concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes the relevance of information theory to entropy in statistical mechanics and mentions its application in approximating functions better than traditional series methods.
  • Several participants recommend introductory texts, including Pierce's "An Introduction to Information Theory" and Stone's "Information Theory: A Tutorial Introduction," while noting a preference for physics-related approaches.
  • A participant highlights Shannon's foundational paper on information theory but suggests it may not be the best starting point for beginners.
  • Another participant recommends A. Katz's "Principles of Statistical Mechanics" as a suitable book for physicists.
  • David MacKay's "Information Theory, Inference, and Learning Algorithms" is mentioned, with emphasis on its discussion of quantifying information and the noisy channel coding theorem.
  • Participants suggest additional resources, including "Statistical Physics of Particles" by Mehran Kardar and "Science and Information Theory" by Leon Brillouin, as well as a paper on Renyi entropy and its applications in physics.
  • James Gleick's "The Information" is recommended for a non-technical but engaging read on the subject.
  • W. T. Grandy's resource letter on information theory in physics is noted as a guide to relevant literature.
  • Participants express varying preferences for different texts, indicating a diversity of perspectives on the best resources.
  • E. T. Jaynes's work linking information theory and statistical mechanics is also recommended by a participant.

Areas of Agreement / Disagreement

Participants generally agree on the importance of information theory in relation to physics and statistical mechanics, but there is no consensus on which resources are the best starting points, as preferences vary widely.

Contextual Notes

Some participants express interest in the physics-related aspects of information theory, while others focus on more general introductions. The discussion reflects a range of expertise and familiarity with the topic, indicating that recommendations may depend on individual backgrounds and interests.

Who May Find This Useful

This discussion may be useful for students and professionals in physics, mathematics, and engineering who are looking to explore the connections between information theory and their fields, as well as those seeking introductory materials on the subject.

AndreasC
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As I've been studying statistical mechanics as well as some other things, I keep hearing about "information theory". For instance, I've heard about information theory as it relates to entropy, regarding some theorems of statistical mechanics, and I even heard about it in a Carl Bender lecture, where he said that you could show using information theory techniques that you could find series that approximate functions or solutions better than Pade or Taylor series etc. I find these things very interesting but I have no idea what to even look for to learn more about the subject, it seems to be one of these categories that different people from different disciplines may use in much different ways. Does anyone have any good sources to gain some understanding?
 
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For me the best book for physicists is

A. Katz, Principles of Statistical Mechanics, W. H. Freeman
and Company, San Francisco and London (1967).
 
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http://www.inference.org.uk/mackay/itprnn/book.html
Information Theory, Inference, and Learning Algorithms
David MacKay

There are two major ideas in information theory, one is the quantification of information, which is closely related to the entropy of statistical physics. In physics, we usually make use of Stirling's approximation. In Mackay's book, you can find the material under the discussion of asymptotic equipartition.

The second major idea is about how well information can be transmitted in the presence of noise. In Mackay's book, it is in the chapter on the noisy channel coding theorem. As far as I understand, this idea is not much used in physics.

Two physics books that discuss basic information theory are

https://www.amazon.com/dp/0521873428/?tag=pfamazon01-20
https://ocw.mit.edu/courses/physics...-fall-2013/lecture-notes/MIT8_333F13_Lec6.pdf (free notes on which the book is based)
Statistical Physics of Particles
Mehran Kardar

https://www.amazon.com/dp/0486497550/?tag=pfamazon01-20
Science and Information Theory
Leon Brillouin

An example of information-like quantities in the research literature is:

https://arxiv.org/abs/1007.4825
Renyi entropy, mutual information, and fluctuation properties of Fermi liquids
Brian Swingle
 
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I love The Information by James Gleick. One of my favorite reads...not technical but fascinating
 
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W. T. Grandy, ‘‘Resource letter ITP-1: Information theory in physics,’’
Am. J. Phys. 65, 466–476 􏰐1997

is a guide to the literature
 
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Elements of information theory by Cover and Thomas is one of the best general texts. Information, physics, and computation by Mezard and Montanari applies ideas from information theory and the physics of disordered systems to computation.

I also second David MacKay’s book.
 
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  • #10
caz said:
W. T. Grandy, ‘‘Resource letter ITP-1: Information theory in physics,’’
Am. J. Phys. 65, 466–476 􏰐1997

is a guide to the literature
Very interesting, I'll check this out first and then look at the rest.
 
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I also highly recommend E. T. Jaynes's Phys Rev article showing the link between information theory and statistical mechanics
Jaynes's papers at Wash U
 
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