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| Format: | Preprint |
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2016
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| Online Access: | https://arxiv.org/abs/1606.08693 |
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| _version_ | 1866915843596615680 |
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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 |
| id |
arxiv_https___arxiv_org_abs_1606_08693 |
| 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 |