One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus of research in physics, going back to the early work of Landauer. One of the most prominent aspects of computers is that they are inherently nonequilibrium systems. However, the early research was done when nonequilibrium statistical physics was in its infancy, which meant the work was formulated in terms of equilibrium statistical physics. Since then there have been major breakthroughs in nonequilibrium statistical physics, which are allowing us to investigate the myriad aspects of the relationship between statistical physics and computation, extending well beyond the issue of how much work is required to erase a bit. In this paper I review some of this recent work on the `stochastic thermodynamics of computation'. After reviewing the salient parts of information theory, computer science theory, and stochastic thermodynamics, I summarize what has been learned about the entropic costs of performing a broad range of computations, extending from bit erasure to loop-free circuits to logically reversible circuits to information ratchets to Turing machines. These results reveal new, challenging engineering problems for how to design computers to have minimal thermodynamic costs. They also allow us to start to combine computer science theory and stochastic thermodynamics at a foundational level, thereby expanding both.

翻译：计算机的主要资源需求之一——从生物细胞到人脑再到高性能（工程）计算机——是运行它们所消耗的能量。执行计算所需的这些成本长期以来一直是物理学研究的焦点，可追溯到Landauer的早期工作。计算机最显著的特征之一是它们本质上是非平衡系统。然而，早期的研究是在非平衡统计物理学尚处于起步阶段时进行的，这意味着相关工作是以平衡统计物理学的框架来阐述的。自那时起，非平衡统计物理学取得了重大突破，使我们能够探究统计物理学与计算之间关系的诸多方面，远远超出了擦除一个比特需要多少功的问题。在本文中，我回顾了近年来关于“计算的随机热力学”的一些工作。在梳理信息论、计算机科学理论和随机热力学的关键部分之后，我总结了关于执行广泛计算（从比特擦除到无环电路、逻辑可逆电路、信息棘轮，再到图灵机）的熵成本的研究成果。这些结果揭示了如何设计具有最小热力学成本的计算机这一新的、具有挑战性的工程问题。同时，它们也使我们能够在基础层面上开始将计算机科学理论与随机热力学结合起来，从而拓展这两个领域。