The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide clas...
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Nature Publishing Group
2016
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4804329/ |
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pubmed-48043292016-03-24 The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics Tirnakli, Ugur Borges, Ernesto P. Article As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results. Nature Publishing Group 2016-03-23 /pmc/articles/PMC4804329/ /pubmed/27004989 http://dx.doi.org/10.1038/srep23644 Text en Copyright © 2016, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Tirnakli, Ugur Borges, Ernesto P. |
| spellingShingle |
Tirnakli, Ugur Borges, Ernesto P. The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| author_facet |
Tirnakli, Ugur Borges, Ernesto P. |
| author_sort |
Tirnakli, Ugur |
| title |
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| title_short |
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| title_full |
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| title_fullStr |
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| title_full_unstemmed |
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics |
| title_sort |
standard map: from boltzmann-gibbs statistics to tsallis statistics |
| description |
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results. |
| publisher |
Nature Publishing Group |
| publishDate |
2016 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4804329/ |
| _version_ |
1613556661655437312 |