Development of Mass and Energy Rate (Density) of Dissipative Systems Over Their Lifetimes: A Comparison of a Low-Mass Star, like Our Sun, a Human, and the Roman Empire

Energy rate density (ERD) corresponds to the energy flow through a dissipative system to maintain its energy gradient and is defined as the energy rate (ER), normalised to mass. ERD has been proposed by Chaisson (2001) as a single, simple metric for complexity of a wide variety of systems over big time. The main objective of this study is to assess the usefulness of this metric over the lifetimes of dissipative systems. For this purpose, mass and ER(D) data have been collected over the lifetimes of a low-mass star, like our Sun, a human, and the Roman Empire, as representative examples of dissipative systems from the cosmological, biological, and cultural realms, respectively. Time profiles of proxies are very useful for further interpretation of the ER(D) time profiles. ER(D) of a low-mass star as a contracting proto-star (< 0.05 Gyr) as well as during its red giant stage and helium flashes (11 to 12.5 Gyr) is much larger than during its stable appearance as a yellow dwarf star in its main sequence (0.05 to 11 Gyr). ERD of a human peaks at 1.5 yr, reflecting the large relative growth of a baby. ER of a human represents the biochemical activities of the human body, especially as a result of physical activities, and reaches a maximum when a human is in the prime of its life between 20 and 30 yr. Cognitive and emotional functions do not impose any additional energy requirements. For the Roman Empire ERD has decreased over time, because the growth rate of the total mass including that of man-made constructs (note that Chaisson only uses mass of humans) was larger than that of ER. ER per capita has hardly varied, because human (slave) labour was the main energy source powering the empire. The Roman Empire was at the height of its power between 100 and 200 CE, which is best reflected by maxima in ER or simply population. Thus, it is concluded that ERD runs in to several issues, when it is applied as a metric of complexity of systems over their lifetimes. ERD does not capture information processing and, as a result, underestimates the complexity of biological and cultural systems. This hampers its application in a BH context, including its use for BH periodisation. Alternative complexity metrics related to information processing need to be developed: information rate density may be a suitable candidate.