This paper has been withdrawn by Airton Deppman Dr.

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Abstract: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 $\Omega_q$ 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.

Submission history

From: Airton Deppman Dr. [view email]
[v1] Tue, 3 Feb 2026 18:33:20 UTC (36 KB)
[v2] Mon, 17 Aug 2026 23:34:28 UTC (1 KB) (withdrawn)