E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics

by E.T. Jaynes (Editor), R. D. Rosenkrantz (Editor)

The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Genres: Mathematics

458 pages, Hardcover

First published January 31, 1983

About the author

Edwin Thompson Jaynes was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical inference, initiating in 1957 the MaxEnt interpretation of thermodynamics, as being a particular application of more general Bayesian/information theory techniques (although he argued this was already implicit in the works of Gibbs). Jaynes strongly promoted the interpretation of probability theory as an extension of logic.
In 1963, together with Fred Cummings, he modelled the evolution of a two-level atom in an electromagnetic field, in a fully quantized way. This model is known as the Jaynes–Cummings model.
A particular focus of his work was the construction of logical principles for assigning prior probability distributions; see the principle of maximum entropy, the principle of transformation groups and Laplace's principle of indifference. Other contributions include the mind projection fallacy.
Jaynes' posthumous book, Probability Theory: The Logic of Science (2003) gathers various threads of modern thinking about Bayesian probability and statistical inference, develops the notion of probability theory as extended logic, and contrasts the advantages of Bayesian techniques with the results of other approaches. This book was published posthumously in 2003 (from an incomplete manuscript that was edited by Larry Bretthorst). An unofficial list of errata is hosted by Kevin S. Van Horn.