Experimental verification of Landauer’s principle linking information and thermodynamics

Journal name:
Nature
Volume:
483,
Pages:
187–189
Date published:
DOI:
doi:10.1038/nature10872
Received
Accepted
Published online

In 1961, Rolf Landauer argued that the erasure of information is a dissipative process1. 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 science2, 3, 4, 5, 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.

At a glance

Figures

  1. The erasure protocol used in the experiment.
    Figure 1: The erasure protocol used in the experiment.

    One bit of information stored in a bistable potential is erased by first lowering the central barrier and then applying a tilting force. In the figures, we represent the transition from the initial state, 0 (left-hand well), to the final state, 1 (right-hand well). We do not show the obvious 1right arrow1 transition. Indeed the procedure is such that irrespective of the initial state, the final state of the particle is always 1. The potential curves shown are those measured in our experiment (Methods).

  2. Erasure cycles and typical trajectories.
    Figure 2: Erasure cycles and typical trajectories.

    a, Protocol used for the erasure cycles bringing the bead from the left-hand well (state 0) to the right-hand well (state 1), and vice versa. b, Protocol used to measure the heat for the cycles in which the bead does not change wells. The reinitialization is needed to restart the measurement, but is not a part of the erasure protocol (Methods). c, Example of a measured bead trajectory for the transition 0right arrow1. d, Example of a measured bead trajectory for the transition 1right arrow1.

  3. Erasure rate and approach to the Landauer limit.
    Figure 3: Erasure rate and approach to the Landauer limit.

    a, Success rate of the erasure cycle as a function of the maximum tilt amplitude, Fmax, for constant Fmaxτ. b, Heat distribution P(Q) for transition 0right arrow1 with τ = 25s and Fmax = 1.89×10−14N. The solid vertical line indicates the mean dissipated heat, left fenceQright fence, and the dashed vertical line marks the Landauer limit, left fenceQright fenceLandauer. c, Mean dissipated heat for an erasure cycle as a function of protocol duration, τ, measured for three different success rates, r: plus signs, r0.90; crosses, r0.85; circles, r0.75. The horizontal dashed line is the Landauer limit. The continuous line is the fit with the function [Aexp(−t/τK)+1]B/τ, where τK is the Kramers time for the low barrier (Methods). Error bars, 1s.d.

References

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Affiliations

  1. Laboratoire de Physique, École Normale Supérieure, CNRS UMR5672 46 Allée d’Italie, 69364 Lyon, France

    • Antoine Bérut,
    • Artak Arakelyan,
    • Artyom Petrosyan &
    • Sergio Ciliberto
  2. Physics Department and Research Center OPTIMAS, University of Kaiserslautern, 67663 Kaiserslautern, Germany

    • Raoul Dillenschneider
  3. Department of Physics, University of Augsburg, 86135 Augsburg, Germany

    • Eric Lutz
  4. Present address: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

    • Eric Lutz

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All authors contributed substantially to this work.

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The authors declare no competing financial interests.

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