Isotropy, entropy, and energy scaling

TL;DR

This paper proposes two principles involving isotropy, entropy, and energy scaling that explain the emergence of complexity and the ubiquitous role of the natural logarithm in the universe.

Contribution

It introduces a novel framework linking degrees of freedom, energy distribution, and networking effects to emergence and the natural logarithm's role.

Findings

Deg(S) = 4/3 Deg(R) in isotropic energy sources

Increased Deg(R) enhances networking effects in R

Universe's isotropic energy distribution predisposes emergence

Abstract

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 1/3 more degrees of freedom relative to R enables R's growth and increasing complexity. Second, rho(R) = Deg(R) times rho(r), where rho(R) represents the collective rate of R and rho(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.