The dissertation main page is here:  Front page.

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Other points of interest:
 

For an explicit derivation and implicit interpretation of both the entropy and the mutual information in terms of state counts and conditional state counts see the section on  entropy and mutual information.

For the mutual information, there is one generalization of particular interest introduced here- the Information Correlation Functions.  These have the powerful interpretation as the information between arbitrary subsets of random variables - fully extending the notion of mutual information to the multiple-random-variable case.

Like puzzles?  Here's an information theoretic puzzler in quantum mechanics.  This section on the information learned about unmeasured observables from measured observables poses and answers the question "how can information about a measurement be learned from another measurement, when making the second measurement precludes making the first?"

A detailed look at information and correlation (and information correlation) in three systems appears in the sections on the bit string system, the Ising system, and the Heisenberg system.  The Heisenberg system demonstrates interesting and startling behavior, where there are broad ranges of the parameter space where the information functions are constant, while making sharp transitions between discrete values.

Pulling information from data is the name of the game.  Contrary to intuition, it is possible with additional data to gain in uncertainty, to become more confused. But, on the average, more data implies more certainty.  These issues are addressed in the section on inference and information.  This work is closely related to later work on Maximally Informative Statistics.

Finally, making good estimates of quantities is at the core of the business.  Information in one observable about another has already been mentioned, and in the sections on the estimation of information functions from data this is addressed in detail.  Here first and second moment estimators for the entropy are developed and compared to frequency-counts estimators for entropy, culminating in the development of estimators for estimators for mutual information, covariance, and chi-squared.

Several routines are provided for symbolic exact-computation of the density of states of the Heisenberg system using the Clebsch-Gordon technology.
 
 

More notes

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