Tsallis Entropy derived from the Chaitin-Kolmogorov Informational Entropy
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917246898536448 |
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| author | Deppman, Airton |
| author_facet | Deppman, Airton |
| contents | We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show that the algorithmic cost follows a power-law of the string length, instead of the linear behaviour obtained in the classical theory. As a result, the Tsallis entropy governs the increase of information. We explore the result showing, through Landauer's limit, that the heat dissipation in systems with long-range correlations is diminished. The $Ω_q$ number, which remains incompressible, now offers the possibility of a continuous increase of complexity, measured by the parameter $q$. We show the consistency of the results by a numerical simulation, and discuss Zipf's law in light of the new findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tsallis Entropy derived from the Chaitin-Kolmogorov Informational Entropy Deppman, Airton Statistical Mechanics Statistics Theory We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show that the algorithmic cost follows a power-law of the string length, instead of the linear behaviour obtained in the classical theory. As a result, the Tsallis entropy governs the increase of information. We explore the result showing, through Landauer's limit, that the heat dissipation in systems with long-range correlations is diminished. The $Ω_q$ number, which remains incompressible, now offers the possibility of a continuous increase of complexity, measured by the parameter $q$. We show the consistency of the results by a numerical simulation, and discuss Zipf's law in light of the new findings. |
| title | Tsallis Entropy derived from the Chaitin-Kolmogorov Informational Entropy |
| topic | Statistical Mechanics Statistics Theory |
| url | https://arxiv.org/abs/2602.03919 |