The theory of stochastic resonance synergies has been written with an attempt to make it a bridge to the mathematical foundation of quantum information electromagnetism. Multidimensional scaling properties of the quantum fields have been derived. The scale-space waves propagate information along multiple dimensions and scales. The calculus of path integration of stochastic resonances has been derived.

In this article, we reflect on some mathematical structures, describing dynamical processes in physics and chemistry. Quantum descriptors of information flow dynamics and binding preferences of atoms and molecules have been studied. The quantum information descriptors come from mirror image analysis of prime number structure distribution. Derived chirality and information geometry have been analyzed, as well.

Synergies of twin primes

The scale-space wave function preserves information about prime number distribution. This structure distribution has been studied algebraically. We have described the 6k+/-1 scale of mirrors in the distribution of twin primes.

Covariant differentials scale multidimensional objects dynamically, in a hierarchy of scale-spaces. These two, rather "parabolic," mirrors make holographic images of objects, resonating information in 5-dimensional scale-spaces.

8 possible cases in triplets of twin primes have been analyzed. A mismatch in the occurrence of a positive prime vs. its negative counterpart inverts the polarity of the scale-space wave function. We denote such a structure as "3-6-9" triplet codes in an analogy to Nikola Tesla's contemplation on how energy and matter distribute in the universe.

Quantum information descriptors and binding preferences

The mathematical structure of prime number distribution translates to the quantum information description of atomic elements and molecules. Describing their group periodic arrangement and binding preferences.

In the limit cases, asymptotic freedom of motion in information flow is coded. The invariance property of the "3-6-9" triplet codes has been described, explaining the polynomial composition of quantum information carriers. The asymptotic freedom of motion corresponds to the so-called "fine structure" constant, in physical interpretation.

Is it all in between "0s" and "1s"?

The Green function of a Lagrangian conserves information in coupled oscillators. Quantum operators, divergence and rotor, shape the scale-space waves. Quantum information electromagnetism binds information carriers in stochastic resonances. The principle of least action is applied in the computation of quadrupoles of information carriers. The calculus of path integration of the stochastic resonances has been derived.

The evolving dynamics of information flow have been analyzed with covariant differentiation. Synergistic exchange of information, carried out by coupled oscillators, allows reversibility in information flow and quantum tunneling. The information (mass-energy) conservation principle is applied dynamically, in 5-dimensional scale-spaces.

Concluding remarks

In this article, we have reflected on the triplet structure of prime number distribution. This algebraic structure of quantum information descriptors and binding preferences makes a bridge to the mathematical foundation of quantum field theory of stochastic resonance synergies.

Periodicity in the arrangement of information carriers in the atomic elements has been described. Derived chirality and geometry of information flow additionally describe its binding preferences in molecular dynamics.

The holographic principle has been applied in expressing multidimensional information in 5-dimensional scale-spaces. Shaping thus connectome of a complex system in the way that conserves information.

References

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