Information Shift Dynamics Described by Tsallis q = 3 Entropy on a Compact Phase Space

Area of Science:

• Statistical Mechanics
• Dynamical Systems Theory
• Mathematical Physics

Background:

• Recent mathematical research links exponential mixing to the Bernoulli property under general conditions.
• Statistical mechanics models often exhibit exponential mixing, providing insights into complex systems.
• Chebyshev maps offer a concrete framework for studying these dynamics.

Purpose of the Study:

• To investigate Bernoulli shift dynamics using Chebyshev maps.
• To explore the maximization of Tsallis entropy (q=3) over Boltzmann-Gibbs entropy (q=1).
• To examine the relevance of information shift dynamics in pre-universal contexts.

Main Methods:

• Analysis of Bernoulli shift dynamics generated by Chebyshev maps of arbitrary order N≥2.
• Investigation of symmetry properties in coupled Chebyshev systems for even and odd N.
• Identification of the fine structure constant as a key coupling constant.

Main Results:

• Chebyshev map dynamics were shown to be exponentially mixing, implying the Bernoulli property.
• The study highlights Tsallis entropy maximization, deviating from standard Boltzmann-Gibbs entropy.
• Symmetry properties were found to differ for even and odd N in coupled systems.
• The fine structure constant (αel=1/137) emerged as a significant coupling constant for N=3, leading to spatial decorrelation.

Conclusions:

• Exponential mixing is a robust consequence of Bernoulli shift dynamics via Chebyshev maps.
• These dynamics and entropy considerations may offer insights into early universe physics.
• The fine structure constant plays a critical role in the behavior of coupled map lattices, particularly for N=3.