PhilSci Archive

The Ergodic Hierarchy, Randomness and Hamiltonian Chaos

Berkovitz, Joseph and Frigg, Roman and Kronz, Fred (2006) The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. [Preprint]

[img]
Preview
PDF
Download (421Kb) | Preview

    Abstract

    Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’ (EH), which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems.


    Export/Citation:EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
    Social Networking:

    Item Type: Preprint
    Keywords: Randomness, ergodic hierarchy, chaos, predictability, dynamical system, correlation
    Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    Depositing User: Roman Frigg
    Date Deposited: 29 Sep 2006
    Last Modified: 07 Oct 2010 11:14
    Item ID: 2927
    URI: http://philsci-archive.pitt.edu/id/eprint/2927

    Actions (login required)

    View Item

    Document Downloads