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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.12712 |
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| _version_ | 1866913723993554944 |
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| author | Okamura, Keisuke |
| author_facet | Okamura, Keisuke |
| contents | The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability mass function is generalised using the $q$-deformed algebra developed within the framework of nonextensive statistics, leading to the emergence of a family of divergence measures in the asymptotic limit as the system size increases. The coefficients in the asymptotic expansion yield Tsallis relative entropy as the leading-order term when $q$ is interpreted as an entropic parameter. Furthermore, higher-order expansion coefficients naturally introduce new divergence measures, extending Tsallis relative entropy through a one-parameter generalisation. Some fundamental properties of these extended divergences are also explored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $q$-generalised multinomial/divergence correspondence Okamura, Keisuke Statistical Mechanics Mathematical Physics The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability mass function is generalised using the $q$-deformed algebra developed within the framework of nonextensive statistics, leading to the emergence of a family of divergence measures in the asymptotic limit as the system size increases. The coefficients in the asymptotic expansion yield Tsallis relative entropy as the leading-order term when $q$ is interpreted as an entropic parameter. Furthermore, higher-order expansion coefficients naturally introduce new divergence measures, extending Tsallis relative entropy through a one-parameter generalisation. Some fundamental properties of these extended divergences are also explored. |
| title | On the $q$-generalised multinomial/divergence correspondence |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2408.12712 |