Maximum Entropy (Most Likely) Double Helical and Double Logarithmic Spiral Trajectories in Space-Time

Area of Science:

• Physics
• Thermodynamics
• Information Theory

Background:

• Double helical and logarithmic spirals are common in nature (e.g., DNA, galaxies).
• The prevalence of these spiral geometries lacks a definitive explanation.
• Geometric entropy provides a potential framework for understanding these structures.

Purpose of the Study:

• To investigate the geometric entropy of double helical and logarithmic spirals.
• To explain the prevalence and stability of these natural structures using information-theoretic principles.
• To connect geometric entropy calculations to the Second Law of Thermodynamics.

Main Methods:

• Complex-vector analysis and Shannon entropy were used to study geometric entropy.
• Calculations were performed for DNA (B-DNA vs. P-DNA Gibbs free energy) and galactic virial mass.
• A novel framework involving conjugate hyperbolic space and entropic momentum coordinates was developed.

Main Results:

• Analytical calculations for DNA and galactic structures align with observational data.
• The developed framework describes spiral structures within a holographic Hamiltonian-Lagrangian system.
• Double spirals were shown to follow a maximum-entropy path, analogous to the principle of least action.

Conclusions:

• The Second Law of Thermodynamics, expressed via geometric entropy, governs the formation of spiral structures.
• These structures represent the most probable and structurally stable geometries in spacetime.
• An entropic action principle, based on Boltzmann's constant, underpins these findings.