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Main Author: Süzen, M.
Format: Preprint
Published: 2016
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Online Access:https://arxiv.org/abs/1606.08693
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author Süzen, M.
author_facet Süzen, M.
contents The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of observable functions-referred to as functional-diffusion. This is not the same as the system's individual trajectories, but can be regarded as a meta-trajectory. Following this idea, we measure how the approach to ergodicity evolves over time for the observed magnetization of a full Ising model with an external field. We compute the diffusive behavior of the functional across a range of temperatures via Metropolis and Glauber single-spin-flip dynamics. The system's ensemble-averaged dynamics are computed using expressions from the exact solution. Power-law behavior in the approach to ergodicity provides a classification of anomalies in functional-diffusion, demonstrating nonlinear anomalous behavior over different temperature and field ranges. Studying the ergodicity convergence of these meta-trajectories can help validate and enhance the pedagogical understanding of nonequilibrium thermodynamic systems.
format Preprint
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institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Anomalous diffusion in convergence to effective ergodicity
Süzen, M.
Statistical Mechanics
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of observable functions-referred to as functional-diffusion. This is not the same as the system's individual trajectories, but can be regarded as a meta-trajectory. Following this idea, we measure how the approach to ergodicity evolves over time for the observed magnetization of a full Ising model with an external field. We compute the diffusive behavior of the functional across a range of temperatures via Metropolis and Glauber single-spin-flip dynamics. The system's ensemble-averaged dynamics are computed using expressions from the exact solution. Power-law behavior in the approach to ergodicity provides a classification of anomalies in functional-diffusion, demonstrating nonlinear anomalous behavior over different temperature and field ranges. Studying the ergodicity convergence of these meta-trajectories can help validate and enhance the pedagogical understanding of nonequilibrium thermodynamic systems.
title Anomalous diffusion in convergence to effective ergodicity
topic Statistical Mechanics
url https://arxiv.org/abs/1606.08693