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

Abstract

Recent mathematical investigations have shown that under very general conditions exponential mixing implies the Bernoulli property. As a concrete example of a statistical mechanics which is exponentially mixing we consider a Bernoulli shift dynamics by Chebyshev maps of arbitrary order $N\ge 2$, which maximizes Tsallis $q=3$ entropy rather than the ordinary $q=1$ Boltzmann-Gibbs entropy. Such an information shift dynamics may be relevant in a pre-universe before ordinary space-time is created. We discuss symmetry properties of the coupled Chebyshev systems, which are different for even and odd $N$. We show that the value of the fine structure constant ${\alpha }_{el}=1/137$ is distinguished as a coupling constant in this context, leading to uncorrelated behaviour in the spatial direction of the corresponding coupled map lattice for $N=3$.

Expanded version; to appear in Entropy

References in corpus (4)

• Modified cosmology from extended entropy with varying exponent
• From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar{p}$ collisions
• Description of High-Energy pp Collisions Using Tsallis Thermodynamics: Transverse Momentum and Rapidity Distributions
• Short chaotic strings and their behaviour in the scaling region