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
Application of the Maximum Entropy Principle to Nonlinear Systems Far from Equilibrium
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. In this paper it is shown how Jaynes' maximum entropy principle or, more generally, his maximum calibre principle can be cast in such a form that the stochastic process that underlies observed data can be determined under the assumption that the process is Markovian. Under suitable constraints it becomes possible to derive the Fokker-Planck equation and the Îto-Langevin equation of that process.
Introduction
Jaynes' maximum entropy principle has found wide-spread applications not only in systems in thermoequilibrium but also in systems far from it. In addition, Jaynes treated time-dependent processes by means of his maximum calibre principle. In the present paper we show how his principles can be cast in such a form that the underlying process that is observed by certain correlation functions can be represented by a Fokker-Planck equation and an Îto-Langevin equation. It will be assumed throughout our paper that the process is Markovian. At the end of this contribution explicit examples treated recently by Lisa Borland and the present author will be presented.
Derivation of the Fokker-Planck Equation
In order to express the definition of a Markov process in a rigorous mathematical form, we choose a time sequence t0, t1, …tM. We may attribute a probability distribution to the path taken by the state vectors at the corresponding times.
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- Chapter
- Information
- Physics and ProbabilityEssays in Honor of Edwin T. Jaynes, pp. 239 - 250Publisher: Cambridge University PressPrint publication year: 1993