Isotropy, entropy, and energy scaling

Two principles explain emergence. First, in the Receipt’s reference frame, Deg(S) = 4 3 Deg(R ), where Supply S is an isotropic radiative energy source, Receipt R receives S’s energy, and Deg is a system’s degrees of freedom based on its mean path length. S’s 3 more degrees of freedom relative to R enables R ’s growth and increasing complexity. Second, ρ(R ) = Deg(R )× ρ(r), where ρ(R ) represents the collective rate of R and ρ(r) represents the rate of an individual in R : as Deg(R ) increases due to the first principle, the multiplier effect of networking in R increases. A universe like ours with isotropic energy distribution, in which both principles are operative, is therefore predisposed to exhibit emergence, and, for reasons shown, a ubiquitous role for the natural logarithm.