Exact Solutions for Small Systems: Urns Models

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Détails bibliographiques
Auteurs principaux:	Hernández-García, Manuel Eduardo, Velázquez-Castro, Jorge
Format:	Preprint
Publié:	2024
Sujets:	Statistical Mechanics Probability 60 G.3
Accès en ligne:	Acceder al recurso
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author	Hernández-García, Manuel Eduardo Velázquez-Castro, Jorge
author_facet	Hernández-García, Manuel Eduardo Velázquez-Castro, Jorge
contents	In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed.
format	Preprint
id	arxiv_https___arxiv_org_abs_2408_11244
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Exact Solutions for Small Systems: Urns Models Hernández-García, Manuel Eduardo Velázquez-Castro, Jorge Statistical Mechanics Probability 60 G.3 In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed.
title	Exact Solutions for Small Systems: Urns Models
topic	Statistical Mechanics Probability 60 G.3
url	https://arxiv.org/abs/2408.11244

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