An improved Landauer principle with finite-size corrections

Reeb, David M.; Wolf, Michael M.

doi:10.1088/1367-2630/16/10/103011

Cited by 285 publications

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“…We then have ∆S S = − ln 2, and the heat emission from S, represented by −Q, is bounded by k B T ln 2 within a small error. While the Landauer principle and its generalizations have been derived in various ways [38,[70][71][72][73][74][75], we here showed that it emerges in the presence of a pure quantum bath.…”

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confidence: 53%

Fluctuation Theorem for Many-Body Pure Quantum States

2017

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We prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy-eigenstate that satisfies the eigenstatethermalization hypothesis (ETH). Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can experimentally be tested by artificial isolated quantum systems such as ultracold atoms.Introduction. Although the microscopic laws of physics do not prefer a particular direction of time, the macroscopic world exhibits inevitable irreversibility represented by the second law of thermodynamics. Modern researches has revealed that even a pure quantum state, described by a single wave function without any genuine thermal fluctuation, can relax to macroscopic thermal equilibrium by a reversible unitary evolution [1][2][3][4][5][6][7][8][9][10][11]. Thermalization of isolated quantum systems, which is relevant to the zeroth law of thermodynamics, is now a very active area of researches in theory [1-6], numerics [10][11][12][13][14][15][16], and experiments [17][18][19][20][21][22][23]. Especially, the concepts of typicality [9,[24][25][26] and the eigenstate thermalization hypothesis (ETH) [10][11][12][27][28][29][30][31][32][33][34][35][36] have played significant roles.However, the second law of thermodynamics, which states that the thermodynamic entropy increases in isolated systems, has not been fully addressed in this context. We would emphasize that the informational entropy (i.e., the von Neumann entropy) of such a genuine quantum system never increases, but is always zero [37]. In this sense, a fundamental gap between the microscopic and macroscopic worlds has not yet been bridged: How does the second law emerge from pure quantum states?In a rather different context, a general theory of the second law and its connection to information has recently been developed even out of equilibrium [38][39][40][41], which has also been experimentally verified in laboratories [42][43][44][45]. This has revealed that information contents and thermodynamic quantities can be treated on an equal footing, as originally illustrated by Szilard and Landauer in the context of Maxwell's demon [46,47]. This research direction invokes a crucial assumption that the heat bath is, at least in the initial time, in the canonical distribution [48]; this special initial condition effectively breaks the

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confidence: 53%

Fluctuation Theorem for Many-Body Pure Quantum States

2017

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“…One can show that the analyzed system thermalizes in Gaussian approximation [12]. This allows to make use of formal expansion over g giving at the leading order: (11) and…”

Section: Finite Time Measurementsmentioning

confidence: 99%

“…More re ned formulation of the principle was given recently in [11]. The authors considered a system immersed into the thermal bath.…”

Section: Introductionmentioning

confidence: 99%

Quantum measurements and Landauer’s principle

Shevchenko

2015

EPJ Web of Conferences

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Abstract. Information processing systems must obey laws of physics. One of particular examples of this general statement is known as Landauer's principle -irreversible operations (such as erasure) performed by any computing device at nite temperature have to dissipate some amount of heat bound from below. Together with other results of this kind, Landauer's principle represents a fundamental limit any modern or future computer must obey.We discuss interpretation of the physics behind the Landauer's principle using a model of Unruh-DeWitt detector. Of particular interest is the validity of this limit in quantum domain. We systematically study nite time e ects. It is shown, in particular, that in high temperature limit niteness of measurement time leads to renormalization of the detector's temperature.

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“…More rigorous and general treatments of this correspondence have been worked out recently [3][4][5]. We first recall this result, and then show how our cost function is a formal extension of this result.…”

Section: Path Space Szilard-landauer Correspondencementioning

confidence: 95%

A Cost/Speed/Reliability Tradeoff to Erasing

Gopalkrishnan

2015

Unconventional Computation and Natural Computation

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Abstract:We present a KL-control treatment of the fundamental problem of erasing a bit. We introduce notions of reliability of information storage via a reliability timescale τ r , and speed of erasing via an erasing timescale τ e . Our problem formulation captures the tradeoff between speed, reliability, and the Kullback-Leibler (KL) cost required to erase a bit. We show that rapid erasing of a reliable bit costs at least log 2 − log 1 − e − τe τr > log 2, which goes to 1 2 log 2τ r τ e when τ r >> τ e .Keywords: Erasing; Information; Thermodynamics; Kullback-Leibler; Optimal control; Reliability; Speed; Tradeoff MotivationBiological systems are remarkably ordered at multiple scales and dimensions, from the spatial order witnessed in the packing of DNA inside the nucleus, the arrangement of cells to form tissues, and organs, and whole organisms, to the temporal order witnessed in the execution of various cellular processes. Superficially such order might appear to violate the second law of thermodynamics which requires an increase in disorder with overwhelmingly high probability. In fact, there is no violation since biological systems expend energy to bring about and maintain this increase in order.We would like to understand this "energy to order" conversion quantitatively. What are the fundamental limits to this conversion? Order can be measured in terms of information, by counting the number of bits required to describe that order. From this point of view, understanding how much energy is required to create order becomes an instance of the investigation of the connection between information processing and thermodynamics. The basic information processing operation that increases order is the operation of "erasing" or resetting a bit to state 0. To fix ideas, imagine erasing random chalk marks from a blackboard, to leave it in a neat and ordered state.Szilard [1] and later Landauer [2] have argued from the second law of thermodynamics that erasing at temperature T requires at least k B T log 2 units of energy, where k B is Boltzmann's constant. The Szilard engine is a simple illustration of this result. Imagine a single molecule of ideal gas in a cylindrical vessel. If this molecule is in the left half of the vessel, think of that as encoding the bit "0," and the bit "1" otherwise. Erasing this Brownian bit corresponds to ensuring that the molecule lies on the left half, for example by compressing the ideal gas to half its volume. For a heuristic analysis we may use the ideal gas law PV = k B T, integrating the expression dW = −PdV for work from limits V to V/2 to obtain W = k B T log 2. More rigorous and general versions of this calculation are known, which also clarify why this is a lower bound [3][4][5].In practice, one finds that both man-made and biological instrumentation often require energy substantially more than k B T log 2 to perform erasing [6,7]. John von Neumann remarked on this large gap in his 1949 lectures at the University of Illinois [8]. (Bennett [9] has remarked that DNA polymerases come ...

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An improved Landauer principle with finite-size corrections

Cited by 285 publications

References 50 publications

Fluctuation Theorem for Many-Body Pure Quantum States

Fluctuation Theorem for Many-Body Pure Quantum States

Quantum measurements and Landauer’s principle

A Cost/Speed/Reliability Tradeoff to Erasing

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