Book contents
- Frontmatter
- Contents
- Preface
- Recollections of an Independent Thinker
- A Look Back: Early Applications of Maximum Entropy Estimation to Quantum Statistical Mechanics
- The Jaynes–Cummings Revival
- The Jaynes–Cummings Model and the One-Atom-Maser
- The Jaynes–Cummings Model is Alive and Well
- Self-Consistent Radiation Reaction in Quantum Optics – Jaynes' Influence and a New Example in Cavity QED
- Enhancing the Index of Refraction in a Nonabsorbing Medium: Phaseonium Versus a Mixture of Two-Level Atoms
- Ed Jaynes' Steak Dinner Problem II
- Source Theory of Vacuum Field Effects
- The Natural Line Shape
- An Operational Approach to Schrödinger's Cat
- The Classical Limit of an Atom
- Mutual Radiation Reaction in Spontaneous Emission
- A Model of Neutron Star Dynamics
- The Kinematic Origin of Complex Wave Functions
- On Radar Target Identification
- On the Difference in Means
- Bayesian Analysis, Model Selection and Prediction
- Bayesian Numerical Analysis
- Quantum Statistical Inference
- Application of the Maximum Entropy Principle to Nonlinear Systems Far from Equilibrium
- Nonequilibrium Statistical Mechanics
- A Backward Look to the Future
- Appendix: Vita and Bibliography of Edwin T. Jaynes
- Index
A Look Back: Early Applications of Maximum Entropy Estimation to Quantum Statistical Mechanics
Published online by Cambridge University Press: 21 October 2009
- Frontmatter
- Contents
- Preface
- Recollections of an Independent Thinker
- A Look Back: Early Applications of Maximum Entropy Estimation to Quantum Statistical Mechanics
- The Jaynes–Cummings Revival
- The Jaynes–Cummings Model and the One-Atom-Maser
- The Jaynes–Cummings Model is Alive and Well
- Self-Consistent Radiation Reaction in Quantum Optics – Jaynes' Influence and a New Example in Cavity QED
- Enhancing the Index of Refraction in a Nonabsorbing Medium: Phaseonium Versus a Mixture of Two-Level Atoms
- Ed Jaynes' Steak Dinner Problem II
- Source Theory of Vacuum Field Effects
- The Natural Line Shape
- An Operational Approach to Schrödinger's Cat
- The Classical Limit of an Atom
- Mutual Radiation Reaction in Spontaneous Emission
- A Model of Neutron Star Dynamics
- The Kinematic Origin of Complex Wave Functions
- On Radar Target Identification
- On the Difference in Means
- Bayesian Analysis, Model Selection and Prediction
- Bayesian Numerical Analysis
- Quantum Statistical Inference
- Application of the Maximum Entropy Principle to Nonlinear Systems Far from Equilibrium
- Nonequilibrium Statistical Mechanics
- A Backward Look to the Future
- Appendix: Vita and Bibliography of Edwin T. Jaynes
- Index
Summary
ABSTRACT. E.T. Jaynes has been the central figure for over three decades in showing how maximum entropy estimation (MEE) provides an extension of logic to cases where one cannot carry out Aristotelian deductive reasoning. Here I will review two early applications of MEE which I hope will provide some insight into how these ideas were being used in quantum and statistical mechanics around 1960.
In May of ‘61 I turned in my Ph.D. thesis (Scalapino, 1961) to Stanford University and, following a well-known dictum, went on to work on other problems. Now, three decades later, on this, the occasion of Ed Jaynes’ seventieth birthday, I decided to look back to see what we were doing when I was first getting to know Ed and his special approach to problems.
Not surprisingly, my thesis contains several applications of the principle of Maximum Entropy Estimation (MEE). In 1957 Ed had written two seminal articles (Jaynes, 1957(a), 1957(b)) showing how one could use Shannon's (1948) Information Theory to construct density matrices for a variety of different problems in equilibrium statistical mechanics. I had been very much taken with this work and wanted to understand how it could be applied to other systems.
- Type
- Chapter
- Information
- Physics and ProbabilityEssays in Honor of Edwin T. Jaynes, pp. 9 - 14Publisher: Cambridge University PressPrint publication year: 1993