Quantum Statistical Dynamics

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The Ricci tensor and the Ricci scalar curvature, in the Einstein field equations, provide scale and curvature limits to

the stress momentum tensor as well as establishing a topological equivalency to the bounds associated with the

Laws of Thermodynamics. Mathematically, Ricci flow, and the Ricci tensor, reduce regions of high curvature and

expand regions of low curvature. Like the “gravity funnel” we associate with topological representations of General

Relativity, (GR), Ricci flow forces the stress tensor, in the field equations, into higher and higher curvatures, limited

by the speed of light and the probabilities we associate with measurements of mass. In this extension of our previous

discussions, we investigate equating Ricci flow, to topological spin at all scales of Lorentz invariance. Using the

topological value that we have established for the Hubble constant, we establish equivalencies to the Metric Tensor

and Einstein’s cosmological constant. We, then, use the field equations to establish topological spin equivalencies to

the Schrodinger equation, the Stefan-Boltzmann equations, Schwarzschild limits at the horizon of a black hole,

Eddington accretion boundaries and measurements of Baryonic Acoustic Oscillations (BAO) in the Cosmic

Microwave Background. In our equivalency to the CMB, we demonstrate how topological spin potentials, associated

with intrinsic global and local phase bifurcation, establish oscillation in the CMB. We establish an equivalency

between Hopf-Turing bifurcation patterns and the development of a dipole moment. To our knowledge, this is the

first application of Hopf-Turing patterns as model for the development of BAO in the CMB. In our final section, we

demonstrate how the field equations, and a topological definition for spin, are all that is necessary to understand

the early appearance SMBH, LRD, Globular Clusters, and Spirals in the early universe.