Article Type: Opinion

Published: January, 2023

DOI: 10.31031/NRS.2023.13.000808

Journal Name: Novel Research in Sciences

Abstract: Our universe involves statistical fields at five major scales that are separated by a factor of 10-17, beginning at exceedingly small Planck scale of 10-35m, electrodynamics 10-18m, hydrodynamics 100 m, astrophysics 1018m, and finally galactic-dynamics (cosmology) 1035m, having “atomic” particles: graviton, electron, fluid element, star, and galaxy [1]. A schematic of hierarchies of statistical fields from photonic to cosmic scale and associated model of embedded dice are shown in Figures 1 & 2. Every statistical field shown in Figure 1 has (atom. element. system) length scales (l, , L) and each statistical system is composed of a spectrum of elements, also called clusters or energy-levels, that contain corresponding spectrum of “atoms”. The question that was asked by both Boltzmann and Planck is: given the total number of atoms N and the total system energy H, what is the distribution of cluster sizes Nj corresponding to stochastically stationary field. Such a state of thermodynamic equilibrium corresponds to energy, speed, and velocity of “atoms” being governed by invariant Planck, Maxwell-Boltzmann, and Gauss (Maxwell) distribution functions [1]. The thermodynamic probability of each level is identified as the inverse of what Boltzmann called number of complexions Wj and is given by [2].