Application of the Thermodynamics of Radiation to Dyson Spheres as Work Extractors and Computational Engines, and their Observational Consequences

TL;DR

This paper applies thermodynamics to Dyson spheres functioning as work and computation devices, deriving efficiency limits and observational signatures, and explores how their structure and properties influence their energy use and detectability.

Contribution

It introduces a formalism for analyzing Dyson spheres as thermodynamic machines, deriving limits on their efficiency, and examining observational consequences with novel insights into their optimal design.

Findings

Small, hot Dyson spheres are generally optimal for energy use.

Optical depths of several are expected in complete Dyson spheres.

Landsberg limit aligns with a form of the Carnot limit for these systems.

Abstract

I apply the thermodynamics of radiation to Dyson spheres as machines that do work or computation, and examine their observational consequences. I identify four properties of Dyson spheres that complicate typical analyses: globally, they may do no work in the usual sense; they use radiation as the source and sink of energy; they accept radiation from a limited range of solid angle; and they conserve energy flux globally. I consider three kinds of activities: computation at the Landauer limit; dissipative activities, in which the energy of a sphere's activities cascades into waste heat, as for a biosphere; and "traditional" work that leaves the sphere, such as radio emission. I apply the Landsberg formalism to derive efficiency limits in all 3 cases, and show that optical circulators provide an "existence proof" that greatly simplifies the problem and allows the Landsberg limit to be plausibly approached. I find that for computation and traditional work, there is little to no advantage to nesting shells (as in a "Matrioshka Brain"); that the optimal use of mass is generally to make very small and hot Dyson spheres; that for "complete" Dyson spheres we expect optical depths of several; and that in all cases the Landsberg limit corresponds to a form of the Carnot limit. I explore how these conclusions might change in the face of complications such as the sphere having practical efficiencies below the Landsberg limit (using the endoreversible limit as an example); no use of optical circulators; and swarms of materials instead of shells.