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In 1961, Rolf Landauer argued that the erasure of information is a dissipative process. A minimal quantity of heat, proportional to the thermal energy and called the Landauer bound, is necessarily produced when a classical bit of information is deleted. A direct consequence of this logically irreversible transformation is that the entropy of the environment increases by a finite amount. Despite its fundamental importance for information theory and computer science, the erasure principle has not been verified experimentally so far, the main obstacle being the difficulty of doing single-particle experiments in the low-dissipation regime. Here we experimentally show the existence of the Landauer bound in a generic model of a one-bit memory. Using a system of a single colloidal particle trapped in a modulated double-well potential, we establish that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles. This result demonstrates the intimate link between information theory and thermodynamics. It further highlights the ultimate physical limit of irreversible computation.

An experimental study of Rayleigh-Bénard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, P r = 0.025), covering a range of Rayleigh numbers 5 × 10 6 < Ra < 5 × 10 9 , and compare them with results at P r ∼ 1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra 0.26 , close to the 2/7 power observed at P r ∼ 1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra 2 × 10 9 , with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for P r ∼ 1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.

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