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Landauer's principle

April 16, 2024

Not to be confused with Landau principle.

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat to its surroundings.[1]

The principle was first proposed by Rolf Landauer in 1961.

Statement edit

Landauer's principle states that the minimum energy needed to erase one bit of information is proportional to the temperature at which the system is operating. More specifically, the energy needed for this computational task is given by

 

where   is the Boltzmann constant.[2] At room temperature, the Landauer limit represents an energy of approximately 0.018 eV (2.9×10−21 J). Modern computers use about a billion times as much energy per operation.[3][4]

History edit

Rolf Landauer first proposed the principle in 1961 while working at IBM.[5] He justified and stated important limits to an earlier conjecture by John von Neumann. For this reason, it is sometimes referred to as being simply the Landauer bound or Landauer limit.

In 2008 and 2009, researchers showed that Landauer's principle can be derived from the second law of thermodynamics and the entropy change associated with information gain, developing the thermodynamics of quantum and classical feedback-controlled systems.[6][7]

In 2011, the principle was generalized to show that while information erasure requires an increase in entropy, this increase could theoretically occur at no energy cost.[8] Instead, the cost can be taken in another conserved quantity, such as angular momentum.

In a 2012 article published in Nature, a team of physicists from the École normale supérieure de Lyon, University of Augsburg and the University of Kaiserslautern described that for the first time they have measured the tiny amount of heat released when an individual bit of data is erased.[9]

In 2014, physical experiments tested Landauer's principle and confirmed its predictions.[10]

In 2016, researchers used a laser probe to measure the amount of energy dissipation that resulted when a nanomagnetic bit flipped from off to on. Flipping the bit required 26 millielectronvolts (4.2 zeptojoules).[11]

A 2018 article published in Nature Physics features a Landauer erasure performed at cryogenic temperatures (T = 1 K) on an array of high-spin (S = 10) quantum molecular magnets. The array is made to act as a spin register where each nanomagnet encodes a single bit of information.[12] The experiment has laid the foundations for the extension of the validity of the Landauer principle to the quantum realm. Owing to the fast dynamics and low "inertia" of the single spins used in the experiment, the researchers also showed how an erasure operation can be carried out at the lowest possible thermodynamic cost—that imposed by the Landauer principle—and at a high speed.[12][13]

Challenges edit

The principle is widely accepted as physical law, but in recent years it has been challenged for using circular reasoning and faulty assumptions, notably in Earman and Norton (1998), and subsequently in Shenker (2000)[14] and Norton (2004,[15] 2011[16]), and defended by Bennett (2003),[1] Ladyman et al. (2007),[17] and by Jordan and Manikandan (2019).[18] Sagawa and Ueda (2008) and Cao and Feito (2009) have shown that Landauer's principle is a consequence of the second law of Thermodynamics and the entropy reduction associated with information gain.[6][7]

On the other hand, recent advances in non-equilibrium statistical physics have established that there is no a priori relationship between logical and thermodynamic reversibility.[19] It is possible that a physical process is logically reversible but thermodynamically irreversible. It is also possible that a physical process is logically irreversible but thermodynamically reversible. At best, the benefits of implementing a computation with a logically reversible system are nuanced.[20]

In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle.[21] However, according to Laszlo Kish (2016),[22] their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode".

See also edit

References edit

  1. ^ a b Charles H. Bennett (2003), "Notes on Landauer's principle, Reversible Computation and Maxwell's Demon" (PDF), Studies in History and Philosophy of Modern Physics, 34 (3): 501–510, arXiv:physics/0210005, Bibcode:2003SHPMP..34..501B, doi:10.1016/S1355-2198(03)00039-X, S2CID 9648186, retrieved 2015-02-18.
  2. ^ Vitelli, M.B.; Plenio, V. (2001). "The physics of forgetting: Landauer's erasure principle and information theory" (PDF). Contemporary Physics. 42 (1): 25–60. arXiv:quant-ph/0103108. Bibcode:2001ConPh..42...25P. doi:10.1080/00107510010018916. eISSN 1366-5812. hdl:10044/1/435. ISSN 0010-7514. S2CID 9092795.
  3. ^ Thomas J. Thompson. . bloomfield knoble. Archived from the original on December 19, 2014. Retrieved May 5, 2013.
  4. ^ Samuel K. Moore (14 March 2012). "Landauer Limit Demonstrated". IEEE Spectrum. Retrieved May 5, 2013.
  5. ^ Rolf Landauer (1961), "Irreversibility and heat generation in the computing process" (PDF), IBM Journal of Research and Development, 5 (3): 183–191, doi:10.1147/rd.53.0183, retrieved 2015-02-18.
  6. ^ a b Sagawa, Takahiro; Ueda, Masahito (2008-02-26). "Second Law of Thermodynamics with Discrete Quantum Feedback Control". Physical Review Letters. 100 (8): 080403. arXiv:0710.0956. Bibcode:2008PhRvL.100h0403S. doi:10.1103/PhysRevLett.100.080403. PMID 18352605. S2CID 41799543.
  7. ^ a b Cao, F. J.; Feito, M. (2009-04-10). "Thermodynamics of feedback controlled systems". Physical Review E. 79 (4): 041118. arXiv:0805.4824. Bibcode:2009PhRvE..79d1118C. doi:10.1103/PhysRevE.79.041118. PMID 19518184. S2CID 30188109.
  8. ^ Joan Vaccaro; Stephen Barnett (June 8, 2011), "Information Erasure Without an Energy Cost", Proc. R. Soc. A, 467 (2130): 1770–1778, arXiv:1004.5330, Bibcode:2011RSPSA.467.1770V, doi:10.1098/rspa.2010.0577, S2CID 11768197.
  9. ^ Antoine Bérut; Artak Arakelyan; Artyom Petrosyan; Sergio Ciliberto; Raoul Dillenschneider; Eric Lutz (8 March 2012), "Experimental verification of Landauer's principle linking information and thermodynamics" (PDF), Nature, 483 (7388): 187–190, arXiv:1503.06537, Bibcode:2012Natur.483..187B, doi:10.1038/nature10872, PMID 22398556, S2CID 9415026.
  10. ^ Yonggun Jun; Momčilo Gavrilov; John Bechhoefer (4 November 2014), "High-Precision Test of Landauer's Principle in a Feedback Trap", Physical Review Letters, 113 (19): 190601, arXiv:1408.5089, Bibcode:2014PhRvL.113s0601J, doi:10.1103/PhysRevLett.113.190601, PMID 25415891, S2CID 10164946.
  11. ^ Hong, Jeongmin; Lambson, Brian; Dhuey, Scott; Bokor, Jeffrey (2016-03-01). "Experimental test of Landauer's principle in single-bit operations on nanomagnetic memory bits". Science Advances. 2 (3): e1501492. Bibcode:2016SciA....2E1492H. doi:10.1126/sciadv.1501492. ISSN 2375-2548. PMC 4795654. PMID 26998519..
  12. ^ a b Rocco Gaudenzi; Enrique Burzuri; Satoru Maegawa; Herre van der Zant; Fernando Luis (19 March 2018), "Quantum Landauer erasure with a molecular nanomagnet", Nature Physics, 14 (6): 565–568, Bibcode:2018NatPh..14..565G, doi:10.1038/s41567-018-0070-7, hdl:10261/181265, S2CID 125321195.
  13. ^ Bennett, Charles H. (September 2003). Notes on Landauer's principle, reversible computation, and Maxwell's Demon. Vol. 34. p. 510. arXiv:physics/0210005. Bibcode:2003SHPMP..34..501B. doi:10.1016/S1355-2198(03)00039-X. ISBN 9780198570493. S2CID 9648186. {{cite book}}: |journal= ignored (help)
  14. ^ Shenker, Orly R. (June 2000). "Logic and Entropy [preprint]". PhilSci Archive. from the original on 15 November 2023. Retrieved 20 December 2023.
  15. ^ Norton, John D. (June 2005). "Eaters of the lotus: Landauer's principle and the return of Maxwell's demon". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 36 (2): 375–411. Bibcode:2005SHPMP..36..375N. doi:10.1016/j.shpsb.2004.12.002. S2CID 21104635. from the original on 5 June 2023. Retrieved 20 December 2023.
  16. ^ Norton, John D. (August 2011). "Waiting for Landauer" (PDF). Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 42 (3): 184–198. Bibcode:2011SHPMP..42..184N. doi:10.1016/j.shpsb.2011.05.002. Retrieved 20 December 2023.
  17. ^ Ladyman, James; Presnell, Stuart; Short, Anthony J.; Groisman, Berry (March 2007). "The connection between logical and thermodynamic irreversibility". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 38 (1): 58–79. Bibcode:2007SHPMP..38...58L. doi:10.1016/j.shpsb.2006.03.007. Retrieved 20 December 2023.
  18. ^ Jordan, Andrew; Manikandan, Sreenath (12 December 2019). "Some Like It Hot". Inference: International Review of Science. 5 (1). doi:10.37282/991819.19.82. S2CID 241470079.
  19. ^ Takahiro Sagawa (2014), "Thermodynamic and logical reversibilities revisited", Journal of Statistical Mechanics: Theory and Experiment, 2014 (3): 03025, arXiv:1311.1886, Bibcode:2014JSMTE..03..025S, doi:10.1088/1742-5468/2014/03/P03025, S2CID 119247579.
  20. ^ David H. Wolpert (2019), "Stochastic thermodynamics of computation", Journal of Physics A: Mathematical and Theoretical, 52 (19): 193001, arXiv:1905.05669, Bibcode:2019JPhA...52s3001W, doi:10.1088/1751-8121/ab0850, S2CID 126715753.
  21. ^ "Computing study refutes famous claim that 'information is physical'". m.phys.org.
  22. ^ Laszlo Bela Kish (2016). "Comments on 'Sub-kBT Micro-Electromechanical Irreversible Logic Gate'". Fluctuation and Noise Letters. 14 (4): 1620001–1620194. arXiv:1606.09493. Bibcode:2016FNL....1520001K. doi:10.1142/S0219477516200017. S2CID 12110986. Retrieved 2020-03-08.

Further reading edit

  • Prokopenko, Mikhail; Lizier, Joseph T. (2014), "Transfer entropy and transient limits of computation", Scientific Reports, 4 (1): 5394, Bibcode:2014NatSR...4E5394P, doi:10.1038/srep05394, PMC 4066251, PMID 24953547

External links edit

Library resources about
Landauer's principle
  • Public debate on the validity of Landauer's principle (conference Hot Topics in Physical Informatics, November 12, 2013)
  • Introductory article on Landauer's principle and reversible computing
  • Maroney, O.J.E. "Information Processing and Thermodynamic Entropy" The Stanford Encyclopedia of Philosophy.
  • Eurekalert.org: "Magnetic memory and logic could achieve ultimate energy efficiency", July 1, 2011

April 16, 2024
landauer, principle, confused, with, landau, principle, physical, principle, pertaining, lower, theoretical, limit, energy, consumption, computation, holds, that, irreversible, change, information, stored, computer, such, merging, computational, paths, dissipa. Not to be confused with Landau principle Landauer s principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation It holds that an irreversible change in information stored in a computer such as merging two computational paths dissipates a minimum amount of heat to its surroundings 1 The principle was first proposed by Rolf Landauer in 1961 Contents 1 Statement 2 History 3 Challenges 4 See also 5 References 6 Further reading 7 External linksStatement editLandauer s principle states that the minimum energy needed to erase one bit of information is proportional to the temperature at which the system is operating More specifically the energy needed for this computational task is given by E kBTln 2 displaystyle E geq k text B T ln 2 nbsp where kB displaystyle k text B nbsp is the Boltzmann constant 2 At room temperature the Landauer limit represents an energy of approximately 0 018 eV 2 9 10 21 J Modern computers use about a billion times as much energy per operation 3 4 History editRolf Landauer first proposed the principle in 1961 while working at IBM 5 He justified and stated important limits to an earlier conjecture by John von Neumann For this reason it is sometimes referred to as being simply the Landauer bound or Landauer limit In 2008 and 2009 researchers showed that Landauer s principle can be derived from the second law of thermodynamics and the entropy change associated with information gain developing the thermodynamics of quantum and classical feedback controlled systems 6 7 In 2011 the principle was generalized to show that while information erasure requires an increase in entropy this increase could theoretically occur at no energy cost 8 Instead the cost can be taken in another conserved quantity such as angular momentum In a 2012 article published in Nature a team of physicists from the Ecole normale superieure de Lyon University of Augsburg and the University of Kaiserslautern described that for the first time they have measured the tiny amount of heat released when an individual bit of data is erased 9 In 2014 physical experiments tested Landauer s principle and confirmed its predictions 10 In 2016 researchers used a laser probe to measure the amount of energy dissipation that resulted when a nanomagnetic bit flipped from off to on Flipping the bit required 26 millielectronvolts 4 2 zeptojoules 11 A 2018 article published in Nature Physics features a Landauer erasure performed at cryogenic temperatures T 1 K on an array of high spin S 10 quantum molecular magnets The array is made to act as a spin register where each nanomagnet encodes a single bit of information 12 The experiment has laid the foundations for the extension of the validity of the Landauer principle to the quantum realm Owing to the fast dynamics and low inertia of the single spins used in the experiment the researchers also showed how an erasure operation can be carried out at the lowest possible thermodynamic cost that imposed by the Landauer principle and at a high speed 12 13 Challenges editThe principle is widely accepted as physical law but in recent years it has been challenged for using circular reasoning and faulty assumptions notably in Earman and Norton 1998 and subsequently in Shenker 2000 14 and Norton 2004 15 2011 16 and defended by Bennett 2003 1 Ladyman et al 2007 17 and by Jordan and Manikandan 2019 18 Sagawa and Ueda 2008 and Cao and Feito 2009 have shown that Landauer s principle is a consequence of the second law of Thermodynamics and the entropy reduction associated with information gain 6 7 On the other hand recent advances in non equilibrium statistical physics have established that there is no a priori relationship between logical and thermodynamic reversibility 19 It is possible that a physical process is logically reversible but thermodynamically irreversible It is also possible that a physical process is logically irreversible but thermodynamically reversible At best the benefits of implementing a computation with a logically reversible system are nuanced 20 In 2016 researchers at the University of Perugia claimed to have demonstrated a violation of Landauer s principle 21 However according to Laszlo Kish 2016 22 their results are invalid because they neglect the dominant source of energy dissipation namely the charging energy of the capacitance of the input electrode See also editMargolus Levitin theorem Bremermann s limit Bekenstein bound Kolmogorov complexity Entropy in thermodynamics and information theory Information theory Jarzynski equality Limits of computation Extended mind thesis Maxwell s demon Koomey s law No deleting theoremReferences edit a b Charles H Bennett 2003 Notes on Landauer s principle Reversible Computation and Maxwell s Demon PDF Studies in History and Philosophy of Modern Physics 34 3 501 510 arXiv physics 0210005 Bibcode 2003SHPMP 34 501B doi 10 1016 S1355 2198 03 00039 X S2CID 9648186 retrieved 2015 02 18 Vitelli M B Plenio V 2001 The physics of forgetting Landauer s erasure principle and information theory PDF Contemporary Physics 42 1 25 60 arXiv quant ph 0103108 Bibcode 2001ConPh 42 25P doi 10 1080 00107510010018916 eISSN 1366 5812 hdl 10044 1 435 ISSN 0010 7514 S2CID 9092795 Thomas J Thompson Nanomagnet memories approach low power limit bloomfield knoble Archived from the original on December 19 2014 Retrieved May 5 2013 Samuel K Moore 14 March 2012 Landauer Limit Demonstrated IEEE Spectrum Retrieved May 5 2013 Rolf Landauer 1961 Irreversibility and heat generation in the computing process PDF IBM Journal of Research and Development 5 3 183 191 doi 10 1147 rd 53 0183 retrieved 2015 02 18 a b Sagawa Takahiro Ueda Masahito 2008 02 26 Second Law of Thermodynamics with Discrete Quantum Feedback Control Physical Review Letters 100 8 080403 arXiv 0710 0956 Bibcode 2008PhRvL 100h0403S doi 10 1103 PhysRevLett 100 080403 PMID 18352605 S2CID 41799543 a b Cao F J Feito M 2009 04 10 Thermodynamics of feedback controlled systems Physical Review E 79 4 041118 arXiv 0805 4824 Bibcode 2009PhRvE 79d1118C doi 10 1103 PhysRevE 79 041118 PMID 19518184 S2CID 30188109 Joan Vaccaro Stephen Barnett June 8 2011 Information Erasure Without an Energy Cost Proc R Soc A 467 2130 1770 1778 arXiv 1004 5330 Bibcode 2011RSPSA 467 1770V doi 10 1098 rspa 2010 0577 S2CID 11768197 Antoine Berut Artak Arakelyan Artyom Petrosyan Sergio Ciliberto Raoul Dillenschneider Eric Lutz 8 March 2012 Experimental verification of Landauer s principle linking information and thermodynamics PDF Nature 483 7388 187 190 arXiv 1503 06537 Bibcode 2012Natur 483 187B doi 10 1038 nature10872 PMID 22398556 S2CID 9415026 Yonggun Jun Momcilo Gavrilov John Bechhoefer 4 November 2014 High Precision Test of Landauer s Principle in a Feedback Trap Physical Review Letters 113 19 190601 arXiv 1408 5089 Bibcode 2014PhRvL 113s0601J doi 10 1103 PhysRevLett 113 190601 PMID 25415891 S2CID 10164946 Hong Jeongmin Lambson Brian Dhuey Scott Bokor Jeffrey 2016 03 01 Experimental test of Landauer s principle in single bit operations on nanomagnetic memory bits Science Advances 2 3 e1501492 Bibcode 2016SciA 2E1492H doi 10 1126 sciadv 1501492 ISSN 2375 2548 PMC 4795654 PMID 26998519 a b Rocco Gaudenzi Enrique Burzuri Satoru Maegawa Herre van der Zant Fernando Luis 19 March 2018 Quantum Landauer erasure with a molecular nanomagnet Nature Physics 14 6 565 568 Bibcode 2018NatPh 14 565G doi 10 1038 s41567 018 0070 7 hdl 10261 181265 S2CID 125321195 Bennett Charles H September 2003 Notes on Landauer s principle reversible computation and Maxwell s Demon Vol 34 p 510 arXiv physics 0210005 Bibcode 2003SHPMP 34 501B doi 10 1016 S1355 2198 03 00039 X ISBN 9780198570493 S2CID 9648186 a href Template Cite book html title Template Cite book cite book a journal ignored help Shenker Orly R June 2000 Logic and Entropy preprint PhilSci Archive Archived from the original on 15 November 2023 Retrieved 20 December 2023 Norton John D June 2005 Eaters of the lotus Landauer s principle and the return of Maxwell s demon Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics 36 2 375 411 Bibcode 2005SHPMP 36 375N doi 10 1016 j shpsb 2004 12 002 S2CID 21104635 Archived from the original on 5 June 2023 Retrieved 20 December 2023 Norton John D August 2011 Waiting for Landauer PDF Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics 42 3 184 198 Bibcode 2011SHPMP 42 184N doi 10 1016 j shpsb 2011 05 002 Retrieved 20 December 2023 Ladyman James Presnell Stuart Short Anthony J Groisman Berry March 2007 The connection between logical and thermodynamic irreversibility Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics 38 1 58 79 Bibcode 2007SHPMP 38 58L doi 10 1016 j shpsb 2006 03 007 Retrieved 20 December 2023 Jordan Andrew Manikandan Sreenath 12 December 2019 Some Like It Hot Inference International Review of Science 5 1 doi 10 37282 991819 19 82 S2CID 241470079 Takahiro Sagawa 2014 Thermodynamic and logical reversibilities revisited Journal of Statistical Mechanics Theory and Experiment 2014 3 03025 arXiv 1311 1886 Bibcode 2014JSMTE 03 025S doi 10 1088 1742 5468 2014 03 P03025 S2CID 119247579 David H Wolpert 2019 Stochastic thermodynamics of computation Journal of Physics A Mathematical and Theoretical 52 19 193001 arXiv 1905 05669 Bibcode 2019JPhA 52s3001W doi 10 1088 1751 8121 ab0850 S2CID 126715753 Computing study refutes famous claim that information is physical m phys org Laszlo Bela Kish 2016 Comments on Sub kBT Micro Electromechanical Irreversible Logic Gate Fluctuation and Noise Letters 14 4 1620001 1620194 arXiv 1606 09493 Bibcode 2016FNL 1520001K doi 10 1142 S0219477516200017 S2CID 12110986 Retrieved 2020 03 08 Further reading editProkopenko Mikhail Lizier Joseph T 2014 Transfer entropy and transient limits of computation Scientific Reports 4 1 5394 Bibcode 2014NatSR 4E5394P doi 10 1038 srep05394 PMC 4066251 PMID 24953547External links editLibrary resources about Landauer s principle Resources in your library Resources in other libraries Public debate on the validity of Landauer s principle conference Hot Topics in Physical Informatics November 12 2013 Introductory article on Landauer s principle and reversible computing Maroney O J E Information Processing and Thermodynamic Entropy The Stanford Encyclopedia of Philosophy Eurekalert org Magnetic memory and logic could achieve ultimate energy efficiency July 1 2011 Retrieved from https en wikipedia org w index php title Landauer 27s principle amp oldid 1215989719, wikipedia, wiki, book, books, library,

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