Here we study the thermodynamic cost of computation and control using ‘physically universal’ cellular automata (CAs) or Hamiltonians. The latter were previously defined as systems that admit the implementation of any desired transformation on a finite target region by first initializing the state of the surrounding and then letting the system evolve according to its autonomous dynamics. This way, one obtains a model of control where each region can play both roles, the controller or the system to be controlled. In physically universal systems every degree of freedom is indirectly accessible by operating on the remaining degrees of freedom.In a nutshell, the thermodynamic cost of an operation is then given by the size of the region around the target region that needs to be initialized. In the meantime, physically universal CAs have been constructed by Schaeffer (in two dimensions) and Salo & Törmä (in one dimension). Here we show that in Schaeffer’s CA the cost for implementing n operations grows linearly in n, while operating in a thermodynamic cycle requires sublinear growth to ensure zero cost per operation in the limit n → ∞. Although this particular result need not hold for general physically universal CAs, this strong notion of universality does imply a certain kind of instability of information, which could result in lower bounds on the cost of protecting information from its noisy environment.The technical results of the paper are sparse and quite simple. The contribution of the paper is mainly conceptual and consists in illustrating the type of thermodynamic questions raised by models of control that rely on the concept of physical universality.

中文翻译：

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物理系统的普遍可控性是否禁止热力学循环？

在这里，我们使用“物理通用”元胞自动机 (CA) 或哈密顿量来研究计算和控制的热力学成本。后者以前被定义为允许在有限目标区域上执行任何所需变换的系统，方法是首先初始化周围的状态，然后让系统根据其自主动态发展。这样，人们就获得了一种控制模型，其中每个区域都可以同时扮演控制器或要控制的系统的角色。在物理通用系统中，每个自由度都可以通过对剩余的自由度进行操作来间接访问。简而言之，操作的热力学成本由目标区域周围需要初始化的区域的大小给出。同时，Schaeffer（二维）和 Salo & Törmä（一维）构建了物理上通用的 CA。在这里，我们展示了在 Schaeffer 的 CA 中，实现 n 次操作的成本在 n 中线性增长，而在热力学循环中运行需要亚线性增长，以确保在极限 n → ∞ 内每次操作的成本为零。虽然这一特定结果不一定适用于一般物理上普遍的 CA，但这种强烈的普遍性概念确实暗示了某种信息的不稳定性，这可能导致保护信息免受其嘈杂环境影响的成本的下限。纸张稀疏且非常简单。