The Ehrenfest fleas: from model to theory
type: Item
instance of: scholarly article
title: The Ehrenfest fleas: from model to theory
zbMATH Open document ID: 1055.60070
published in: Synthese
publication date: 2004-08-06T00:00:00Z
review text: The authors propose a generalized Ehrenfest urn model (i.e., \(n\) individuals distributed on \(d\) categories) and develop an abstract theory based on some axioms for the conditional probability \(\text{Pr}\{n(j)| n\}\), where the occupation vector \(n= (n_1,\dots, n_d)\in N^n_d\), \(\sum^d_{j=1} n_j= n\), and \(n(j)\) is the occupation vector resulted from \(n\) increasing or decreasing by \(1\) at the \(j\)th category (\(n(j)\in N^{n+1}_d\) or \(N^{n-1}_d\)). In fact, the exchangeability and invariance (for increasing or decreasing) are assumed in these axioms. Under some additional simple conditions the generalized model yields transition probability and equilibrium distribution. It then can lead to the unified statistics of Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann and can also follow many applications in population genetics, economics etc. This paper strongly means that the time evolution or explication of many natural phenomena can be given in terms of conditional probabilities, which play an essential role in science.
reviewed by: Chengxun Wu
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2081517
zbMATH Keywords: Ehrenfest urn model
zbMATH Keywords: Brillouin's approach
zbMATH Keywords: conditional probability
zbMATH Keywords: transition probability
zbMATH Keywords: equilibrium distribution
zbMATH Keywords: statistical mechanics
author: D. Costantini
author: U. Garibaldi
MaRDI profile type: Publication
full work available at URL: b:synt.0000021307.64103.b8
OpenAlex ID: W2016072539
DOI: 10.1023/B:SYNT.0000021307.64103.B8
description: scientific article; zbMATH DE number 2081517