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Some physical processes, including the intensity fluctuations of a chaoticlaser, the detection of single photons, and the Brownian motion of amicroscopic particle in a fluid are unpredictable, at least on long timescales.This unpredictability can be due to a variety of physical mechanisms, but it isquantified by an entropy rate. This rate describes how quickly a systemproduces new and random information, is fundamentally important in statisticalmechanics and practically important for random number generation. Weexperimentally study entropy generation and the emergence of deterministicchaotic dynamics from discrete noise in a system that applies feedback to aweak optical signal at the single-photon level. We show that the dynamicsqualitatively change from shot noise to chaos as the photon rate increases, andthat the entropy rate can reflect either the deterministic or noisy aspects ofthe system depending on the sampling rate and resolution.

Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop