A Road to Randomness in Physical Systems

A Road to Randomness in Physical Systems by Eduardo M.R.A. Engel.

There are many ways of introducing the concept of probability in classical, i. e, deter­ ministic, physics. This work is concerned with one approach, known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930's. The idea is...

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Bibliographic Details
Main Author: Engel, Eduardo M.R.A (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1992.
Edition:1st ed. 1992.
Series:Lecture Notes in Statistics, 71
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Introduction
  • 1.1 The Simple Harmonic Oscillator
  • 1.2 Philosophical Interpretations
  • 1.3 Coupled Harmonic Oscillators
  • 1.4 Mathematical Results
  • 1.5 Calculating Rates of Convergence
  • 1.6 Hopf’s Approach
  • 1.7 Physical and Statistical Independence
  • 1.8 Statistical Regularity of a Dynamical System
  • 1.9 More Applications
  • 2 Preliminaries
  • 2.1 Basic Notation
  • 2.2 Weak-star Convergence
  • 2.3 Variation Distance
  • 2.4 Sup Distance
  • 2.5 Some Concepts from Number Theory
  • 3 One Dimensional Case
  • 3.1 Mathematical Results
  • 3.2 Applications
  • 4 Higher Dimensions
  • 4.1 Mathematical Results
  • 4.2 Applications
  • 5 Hopf’s Approach
  • 5.1 Force as a Function of Only Velocity: One Dimensional case
  • 5.2 Force as a Function of Only Velocity: Higher Dimensions
  • 5.3 The Force also Depends on the Position
  • 5.4 Statistical Regularity of a Dynamical System
  • 5.5 Physical and Statistical Independence
  • 5.6 The Method of Arbitrary Functions and Ergodic Theory
  • 5.7 Partial Statistical Regularity
  • 6 Non Diagonal Case
  • 6.1 Mathematical Results
  • 6.2 Linear Differential Equations
  • 6.3 Automorphisms of the n-dimensional Torus
  • References.

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