Dissipative systems have a maximum energy rate density of 105 W/kg

Abstract

Mass and energy rate (ER) data have been collected for a wide variety of dissipative systems from the biological, cultural, and cosmological realms. They range from 6 × 10^–25 kg and 3 × 10^–25 W for a synthetic, molecular engine to 1.5 × 10⁵³ kg and 10⁴⁸ W for the observable universe and, thus, span 78 mass and 73 ER orders of magnitude, respectively. The combination of (i) convergence of smaller systems (parts) to a larger system and (ii) scaling of ER as a function of mass with a power law constant β > 0 for groups of systems, explains why the ER and mass data points fall in a diagonal band in the double logarithmic ER vs. mass master plot. There appears to be an ER vs. mass limit, corresponding to an energy rate density (ERD = ER/mass) of around 10⁵ W/kg, separating stable, dissipative systems from unstable, “explosive” systems (atomic weapons, supernova, etc.) in all realms. This limit is probably the result of a balance between the energy flow through a system, resulting in increased temperature and pressure, and the strength of the system’s structure and boundary. ERD has been proposed as a metric for the development of the complexity of dissipative systems over deep time Chaisson (Cosmic evolution; The rise of complexity in nature. Harvard University Press, Cambridge, 2002), Chaisson (Sci World J 384912, 2014). Thus, the observed ERD threshold of 10⁵ W/kg may correspond to a maximum of complexity. Several ways to further increase complexity while circumventing this ERD limit are proposed.

Graphical abstract