## On Nonextensive Statistics, Chaos and Fractal Strings

**Authors:** Carlos Castro

Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the
Tsallis non-extensive statistics (with a non-additive q-entropy) of an ensemble of fractal strings and branes
of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may
exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis
statistics is a particular representative of such class. The non-extensive entropy and probability distribution
of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which
leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy
and temperature. The absolute zero temperature (Kelvin) corresponds to zero dimensions (energy) and
an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications
of fractal statistics, quasi-particles, knot theory, quantum groups and number theory are briefly discussed
within the framework of fractal strings and branes.

**Comments:** 16 pages, This article appeared in Physica A 347 (2005) 184-204

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### Submission history

[v1] 3 Sep 2009

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