辐射热力学在戴森球作为功提取器和计算引擎中的应用及其观测结果

Jason T. Wright
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引用次数: 0

摘要

我将辐射热力学应用于戴森球作为做功或计算的机器,并检查它们的观测结果。我确定了戴森球的四个特性,使典型的分析复杂化:从整体上看,它们可能在通常意义上不起作用;它们利用辐射作为能量的来源和汇;它们接受来自有限立体角范围的辐射;它们保存了全球的能量流动。我考虑了三种活动:在兰道尔极限下的计算;耗散活动,其中一个球体活动的能量级联成废热,如生物圈;而“传统”的工作则离开了地球,比如无线电发射。我运用兰茨伯格的形式推导了所有三种情况下的效率极限,并证明了光环路提供了一个“存在性证明”,极大地简化了问题,并允许兰茨伯格极限被合理地接近。我发现对于计算和传统工作来说,测试shell(如“Matrioshka Brain”)几乎没有任何优势;质量的最佳利用通常是制造非常小而热的戴森球;对于“完全的”非球形球体,我们预计光学深度为几个;在所有情况下,兰氏极限都对应于卡诺极限的一种形式。我探讨了这些结论在面对复杂情况时可能发生的变化,例如球体的实际效率低于兰茨贝格极限(以不可逆极限为例);不使用光学循环器;还有成堆的材料,而不是贝壳。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Application of the Thermodynamics of Radiation to Dyson Spheres as Work Extractors and Computational Engines, and their Observational Consequences
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.
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