Buffon's Brownian needles: harnessing thermal motion for stochastic sampling

Abstract

We demonstrate a physical implementation of Monte Carlo sampling using the Brownian motion of microscopic rods, applied to the classical Buffon's needle experiment. In this way, a problem in geometric probability is mapped onto a Monte Carlo method, with a physical system performing key aspects of the computation. The experiment's parameters are embedded directly: the rods length encodes the probability integral, while their thermal motion supplies the sampling. Although only a toy-model system, this approach illustrates how embedding probabilistic structure into soft matter can provide a low-energy pathway for stochastic computation that exploits freely available thermal noise.