Entropy and its relationship to allometry

TL;DR

This paper explores the mathematical relationship between entropy, allometry, and biological and cosmological scaling laws, proposing that the 4/3 power scaling explains cellular metabolism and dark energy.

Contribution

It introduces a mathematical framework linking entropy scaling to biological and cosmological phenomena, highlighting the 4/3 power law as a unifying principle.

Findings

Metabolic rate scales inversely with 3/4 power of mass.

Energy supply capacity scales with 4/3 power of size.

Potential explanation for dark energy through entropy scaling.

Abstract

Researchers have found that the metabolisms of organisms appear to scale proportionally to a 3/4 power of their mass. Mathematics in this article suggests that the capacity of an isotropically radiating energy supply scales up by a 4/3 power as its size (and therefore the degrees of freedom of its circulatory system) increases. Accordingly, cellular metabolism scales inversely by a 3/4 power, likely to prevent the 4/3 scaling up of the energy supply overheating the cell. The same 4/3 power scaling may explain cosmological dark energy.