We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different algorithm, is for Boolean matrix multiplication. We hope this work inspires a deeper consideration of physically plausible/realizable models of computing that might allow for algorithms which improve upon the runtimes and energy usages suggested by the parallel RAM model in which each operation requires one unit of time and one unit of energy.

翻译：我们描述了两种在经典物理基本模型下使用时间与能量为n² polylog(n)的n×n矩阵乘法算法。第一种算法用于整数值矩阵乘法，第二种截然不同的算法用于布尔矩阵乘法。希望这项工作能启发学界更深入地思考物理上可行/可实现的计算模型，这些模型或可允许算法突破并行随机存取机模型（其中每次操作消耗一个时间单位和一个能量单位）所建议的运行时间和能耗上限。