Irreversibility and heat generation in the computing process

Landauer, Rolf

doi:10.1147/rd.441.0261

Cited by 1,546 publications

(1,770 citation statements)

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“…As an example, the statement of the second law of thermodynamics in the presence of an ancilla [1,2] or, when the system has coherence [3,4], has been established in great details, from where the classical version of the second law emerges under appropriate limits. The study of thermodynamics in quantum domain can be approached from different directions such as information-theoretic point of view [5][6][7][8][9][10] or resource-theoretic aspect [11][12][13]. Another important constituent, in this area of study, is the work extraction from quantum systems [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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Abstract:We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples; coupled spin-1/2 systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-1/2 systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus, the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.

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Section: Introductionmentioning

confidence: 99%

Implications of Coupling in Quantum Thermodynamic Machines

Thomas

Banik

Ghosh

2017

Entropy

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“…1 Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Tokyo 112-8551, Japan, 2 Department of Physics, Graduate School of Science, University of Tokyo, Hongo, Tokyo 113-0033, Japan, 3 ERATO Macroscopic Quantum Control Project, JST, Yayoi, Tokyo 113-8656, Japan. *e-mail: emuneyuk@phys.chuo-u.ac.jp; sano@phys.s.u-tokyo.ac.jp.…”

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confidence: 99%

“…As the energy converted from information is compensated for by the demon's energy cost to manipulate information [2][3][4] , the second law of thermodynamics is not violated when the total system including both the particle and demon is considered. In our system, the demon consists of macroscopic devices such as computers; the microscopic device gains energy at the expense of the energy consumption of a macroscopic device.…”

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confidence: 99%

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

et al. 2010

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In 1929, Leó Szilárd invented a feedback protocol 1 in which a hypothetical intelligence-dubbed Maxwell's demon-pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy 2-6 . An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using realtime feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality 7 , and suggests a new fundamental principle of an 'information-to-heat engine' that converts information into energy by feedback control.To illustrate the basic idea of our feedback protocol, let us consider a microscopic particle on a spiral-staircase-like potential ( Fig. 1). We set the height of each step comparable to the thermal energy k B T , where k B is the Boltzmann constant and T is temperature. Subjected to thermal fluctuations, the particle jumps between steps stochastically. Although the particle sometimes jumps to an upper step, downward jumps along the gradient are more frequent than upward jumps. In this manner, on average, the particle falls down the stairs unless it is externally pushed up (Fig. 1a). Now, let us consider the following feedback control: We measure the particle's position at regular intervals, and if an upward jump is observed we place a block behind the particle to prevent subsequent downward jumps (Fig. 1b). If this procedure is repeated, the particle is expected to climb up the stairs. Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. In such a case, what drives the particle to climb up the stairs? This apparent contradiction to the second law of thermodynamics, epitomized by Maxwell's demon, inspired many physicists to generalize the principles of thermodynamics 1,5,6 . It is now understood that the particle is driven by the 'information' gained by the measurement of the particle's location 5,8 .In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant but particle on a spiral-staircase-like potential with a step height comparable to k B T. The particle stochastically jumps between steps owing to thermal fluctuations. As the downward jumps along the gradient are more frequent than the upward ones, the particle falls down the stairs, on average. b, Feedback control. When an upward jump is observed, a block is placed behind the particle to prevent downward jumps. By repeating ...

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“…Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal sensing with four orders of magnitude improved thermal sensitivity of below 1 µK/Hz 1/2 . The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit [16][17][18] of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of dissipation due to single electron charging of individual quantum dots in carbon nanotubes and reveal a novel dissipation mechanism due to resonant localized states in hBN encapsulated graphene, opening the door to direct imaging of nanoscale dissipation processes in quantum matter. 2 Investigation of energy dissipation on the nanoscale is of major fundamental interest for a wide range of disciplines from biological processes, through chemical reactions, to energy-efficient computing [1][2][3][4][5] .…”

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confidence: 99%

Nanoscale thermal imaging of dissipation in quantum systems

Halbertal

Cuppens

Shalom

et al. 2016

Nature

190

175

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Energy dissipation is a fundamental process governing the dynamics of physical, chemical, and biological systems. It is also one of the main characteristics distinguishing quantum and classical phenomena. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance the microscopic behavior of a system is usually not formulated in terms of dissipation because the latter is not a readily measureable quantity on the microscale. Although nanoscale thermometry is gaining much recent interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] , the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation required for study of quantum systems. Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal sensing with four orders of magnitude improved thermal sensitivity of below 1 µK/Hz 1/2 . The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit [16][17][18] of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of dissipation due to single electron charging of individual quantum dots in carbon nanotubes and reveal a novel dissipation mechanism due to resonant localized states in hBN encapsulated graphene, opening the door to direct imaging of nanoscale dissipation processes in quantum matter. 2 Investigation of energy dissipation on the nanoscale is of major fundamental interest for a wide range of disciplines from biological processes, through chemical reactions, to energy-efficient computing [1][2][3][4][5] . Study of dissipation mechanisms in quantum systems is of particular importance because dissipation demolishes quantum information. In order to preserve a quantum state the dissipation has to be extremely weak and hence hard to measure. As a figure of merit for detection of low power dissipation in quantum systems 16 we consider an ideal qubit operating at a typical readout frequency of 1 GHz. Landauer's principle states the lowest bound on energy dissipation in an irreversible qubit operation to be 0 = B ln 2, where B is Boltzmann's constant and is the temperature 17,18 . At = 4.2 K, 0 = 410 -23 J, several orders of magnitude below 10 -19 J of dissipation per logical operation in present day superconducting electronics and 10 -15 J in CMOS devices 19,20 . Hence the power dissipated by an ideal qubit operating at a readout rate of = 1 GHz will be as low as = 0 = 40.2 fW. The resulting temperature increase of the qubit will depend on its size and the thermal properties of the substrate. For example, a 120 × 120 nm 2 device on a 1 µm thick SiO 2 /Si substrate dissipating 40 fW will heat up by about 3 µK (Fig. 1). Suc...

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Irreversibility and heat generation in the computing process

Cited by 1,546 publications

References 2 publications

Implications of Coupling in Quantum Thermodynamic Machines

Implications of Coupling in Quantum Thermodynamic Machines

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

Nanoscale thermal imaging of dissipation in quantum systems

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