Information and thermodynamics: experimental verification of Landauer's Erasure principle

Bérut, Antoine; Petrosyan, Artyom; Ciliberto, S.

doi:10.1088/1742-5468/2015/06/p06015

Cited by 53 publications

(57 citation statements)

References 27 publications

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“…The final state, 4 after time τ , is in local equilibrium with probability p τ to be in the left well, corresponding to H τ between zero and one bit. Thus, ∆H = H τ − 1 andThis protocol resembles that used in [60,65,66]. However, in those studies, partial erasure was used because the barrier could not be made high enough to ensure full erasure, and correction factors were applied to infer the work required for full erasure of a bit.…”

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confidence: 99%

“…Or, we can selectively stretch one well by a factor η while the other well is unchanged. Such manipulations are not possible in erasure experiments based on optical tweezers [60,65,66], which limits the possible protocols in such cases.The challenge with using feedback traps to measure work values to an accuracy < 0.1 k B T is to calibrate forces accurately and to account for slow drifts in quantities such as the particle's response to an applied voltage. In earlier work, we developed a recursive, real-time calibration technique [73] that allows us to measure accurately the stochastic work done by a changing potential 6 on a particle.…”

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confidence: 99%

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Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

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Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here, for the first time, we measure experimentally this function. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a twostate system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds. INTRODUCTIONBeginning with the foundational work of Clausius, Maxwell, and Boltzmann in the 19th c., the concept of entropy has played a key role in thermodynamics. Yet, despite its importance, entropy is an elusive concept [1][2][3][4][5][6][7][8], with no unique definition; rather, the appropriate definition of entropy depends on the scale, relevant thermodynamic variables, and nature of the system, with ongoing debate existing over the proper definition even for equilibrium cases [9]. Moreover, entropy has not been directly measured but is rather inferred from other quantities, such as the integral of the specific heat divided by temperature. Here, by measuring the work required to erase a fraction of a bit of information, we isolate directly the change in entropy in an open nonequilibrium system, showing that it is compatible with the functional form proposed by Gibbs and Shannon, giving it a physical meaning in this context. Knowing the relevant form of entropy is crucial for efforts to extend thermodynamics to systems out of equilibrium.For a continuous classical system whose state in phase space x is distributed as the probability density function ρ(x), the Gibbs-Shannon entropy is [10,11] where k B is Boltzmann's constant. For quantum systems, von Neumann introduced, in 1927, the corresponding expression in terms of the density matrix [12]. Historically, the system in Eq. 1 has typically been assumed to be in thermal equilibrium. * email: johnb@sfu.caThe physical relevance of Eq. 1 for a nonequilibrium distribution ρ(x) has often been questioned (e.g., [13][14][15][16][17]). One concern is that S is constant on an isolated Hamiltonian system and can change only when evaluated on subsystems, such as those picked out by coarse graining. With many ways to choose subsystems or to coarse grain, is the associated notion of irreversibility intrinsic to the description of the system?In another approach to entropy, advanced in the context of communication and information theory, Shannon [11,18] proved that, up to a multiplicative constant, S is the only possible function satisfying three intuitive axioms. Alternatively, one can start from an...

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confidence: 99%

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confidence: 99%

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…We have implemented the TESE expansion protocol on a Brownian particle trapped by an optical tweezer [29]. Our experimental system consists of a silica microsphere of radius R = 1 µm (±5%) immersed in water.…”

Section: Pacs Numbersmentioning

confidence: 99%

Thermal bath engineering for swift equilibration

et al. 2018

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We provide a theoretical and experimental protocol that dynamically controls the effective temperature of a thermal bath, through a well-designed noise engineering. We use this powerful technique to shortcut the relaxation of an overdamped Brownian particle in a quadratic potential by a joint time engineering of the confinement strength and of the noise. For an optically trapped colloid, we report an equilibrium recovery time reduced by about two orders of magnitude compared to the natural relaxation time. Our scheme paves the way towards reservoir engineering in nanosystems.

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“…The choice of p 0 (x 0 ) is not compatible with our original derivation of the fluctuation theorem (17), which assumes that it is everywhere nonzero. But we can recover a sensible expression if we restrict our domain of integration to trajectories that begin in I and end in II [10,75]. This yields: (24) where π(I → II) is the normalization of the trajectory distribution over the restricted domain…”

Section: B Statistical Irreversibility In Macroscopic Transitionsmentioning

confidence: 99%

Limits of predictions in thermodynamic systems: a review

Marsland

England

2017

Rep. Prog. Phys.

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The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental constraints on the dynamics of systems arbitrarily far from thermal equilibrium. Thermodynamic uncertainty relations bound the dissipative cost of precision in a wide variety of processes. Concepts of excess work and excess heat provide the basis for a complete thermodynamics of nonequilibrium steady states, including generalized Clausius relations and thermodynamic potentials. But these general results carry their own limitations: fluctuation theorems involve exponential averages that can depend sensitively on unobservably rare trajectories; steady-state thermodynamics makes use of a dual dynamics that lacks any direct physical interpretation. This review aims to present these central results of contemporary nonequilibrium thermodynamics in such a way that the power of each claim for making physical predictions can be clearly assessed, using examples from current topics in soft matter and biophysics.

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Information and thermodynamics: experimental verification of Landauer's Erasure principle

Cited by 53 publications

References 27 publications

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Thermal bath engineering for swift equilibration

Limits of predictions in thermodynamic systems: a review

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