论文标题
熵，对称性和自我复制的困难
Entropy, Symmetry, and the Difficulty of Self-Replication
论文作者
论文摘要
人工物理自我复制系统的定义特性，例如自我复制机器人，是它具有从基本部分中复制自身的能力。在研究此类系统中立即出现的三个问题是：1）与每个基本部分相比，整个机器人的复杂程度有多复杂？ 2）在成功复制机器人时，这些零件会多么混乱？ 3）哪些设计原理可以使复杂的自我复制系统在一代后的生成无序环境中发挥作用？因此，本文的大部分都集中在探索熵的不同概念上，以衡量疾病的量度，以及对称性如何在组装级别（通过减少可以组装的零件的错误方式数量）以及作为奇偶校验检查时，何时复制何时生产零件。通过整合信息理论，统计力学，ergodic理论，群体理论和整体几何形状的思想，在此阐明了这些量化人为物理自我复制系统的原则的基础的数学。
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such systems are: 1) How complex is the whole robot in comparison to each basic part ? 2) How disordered can the parts be while having the robot successfully replicate ? 3) What design principles can enable complex self-replicating systems to function in disordered environments generation after generation ? Consequently, much of this article focuses on exploring different concepts of entropy as a measure of disorder, and how symmetries can help in reliable self replication, both at the level of assembly (by reducing the number of wrong ways that parts could be assembled), and also as a parity check when replicas manufacture parts generation after generation. The mathematics underpinning these principles that quantify artificial physical self-replicating systems are articulated here by integrating ideas from information theory, statistical mechanics, ergodic theory, group theory, and integral geometry.
