Landauer's principle

{{Short description|Physical lower limit to energy consumption of computation}}

Landauer's principle is a physical principle pertaining to a 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.{{Citation |arxiv=physics/0210005 |title=Notes on Landauer's principle, Reversible Computation and Maxwell's Demon |authorlink=Charles H. Bennett (computer scientist) |author=Charles H. Bennett |journal=Studies in History and Philosophy of Modern Physics |volume=34 |issue=3 |pages=501–510 |year=2003 |url=http://www.cs.princeton.edu/courses/archive/fall06/cos576/papers/bennett03.pdf |accessdate=2015-02-18 |doi=10.1016/S1355-2198(03)00039-X |bibcode=2003SHPMP..34..501B |s2cid=9648186 }}. It is hypothesized that energy consumption below this lower bound would require the development of reversible computing.

The principle was first proposed by Rolf Landauer in 1961.

Statement

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. Specifically, the energy needed for this computational task is given by

: $E \geq k_\text{B} T \ln 2,$

where $k_\text{B}$ is the Boltzmann constant and $T$ is the temperature in Kelvin.{{cite journal|title=The physics of forgetting: Landauer's erasure principle and information theory|journal=Contemporary Physics|volume=42|issue=1|doi=10.1080/00107510010018916|pages=25–60|issn=0010-7514|eissn=1366-5812|last1=Vitelli|first1=M.B.|last2=Plenio|first2=V.|date=2001|url=http://www3.imperial.ac.uk/pls/portallive/docs/1/55905.PDF|arxiv=quant-ph/0103108|bibcode=2001ConPh..42...25P|hdl=10044/1/435|s2cid=9092795}} At room temperature, the Landauer limit represents an energy of approximately {{convert|0.018|eV|J|abbr=on}}. {{as of|2012}}, modern computers use about a billion times as much energy per operation.{{cite web |url=http://www.bloomweb.com/nanomagnet-memories-approach-low-power-limit/ |author=Thomas J. Thompson |title=Nanomagnet memories approach low-power limit |website=bloomfield knoble |date= |accessdate=May 5, 2013 |archive-url=https://web.archive.org/web/20141219043239/http://www.bloomfieldknoble.com/nanomagnet-memories-approach-low-power-limit/ |archive-date=December 19, 2014 |url-status=dead}}{{cite web |url=https://spectrum.ieee.org/landauer-limit-demonstrated |author= Samuel K. Moore |title=Landauer Limit Demonstrated |website=IEEE Spectrum |date=14 March 2012 |access-date=May 5, 2013}}

History

Rolf Landauer first proposed the principle in 1961 while working at IBM.{{Citation |author=Rolf Landauer |url=http://worrydream.com/refs/Landauer%20-%20Irreversibility%20and%20Heat%20Generation%20in%20the%20Computing%20Process.pdf |title=Irreversibility and heat generation in the computing process |journal=IBM Journal of Research and Development |volume=5 |issue=3 |pages=183–191 |year=1961 |accessdate=2015-02-18 |doi=10.1147/rd.53.0183 }}. He justified and stated important limits to an earlier conjecture by John von Neumann. This refinement is sometimes called 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.{{Cite journal |last1=Sagawa |first1=Takahiro |last2=Ueda |first2=Masahito |date=2008-02-26 |title=Second Law of Thermodynamics with Discrete Quantum Feedback Control |url=https://link.aps.org/doi/10.1103/PhysRevLett.100.080403 |journal=Physical Review Letters |volume=100 |issue=8 |pages=080403 |doi=10.1103/PhysRevLett.100.080403|pmid=18352605 |arxiv=0710.0956 |bibcode=2008PhRvL.100h0403S |s2cid=41799543 }}{{Cite journal |last1=Cao |first1=F. J. |last2=Feito |first2=M. |date=2009-04-10 |title=Thermodynamics of feedback controlled systems |url=https://link.aps.org/doi/10.1103/PhysRevE.79.041118 |journal=Physical Review E |volume=79 |issue=4 |pages=041118 |doi=10.1103/PhysRevE.79.041118|pmid=19518184 |arxiv=0805.4824 |bibcode=2009PhRvE..79d1118C |s2cid=30188109 }}

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.{{Citation |author1=Joan Vaccaro |author2=Stephen Barnett |title=Information Erasure Without an Energy Cost |journal=Proc. R. Soc. A |date=June 8, 2011 |volume=467 |issue=2130 |pages=1770–1778 |doi=10.1098/rspa.2010.0577 |arxiv=1004.5330 |bibcode = 2011RSPSA.467.1770V |s2cid=11768197 }}. 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.{{Citation |author1=Antoine Bérut |author2=Artak Arakelyan |author3=Artyom Petrosyan |author4=Sergio Ciliberto |author5=Raoul Dillenschneider |author6=Eric Lutz |doi=10.1038/nature10872 |title=Experimental verification of Landauer's principle linking information and thermodynamics |journal=Nature |volume=483 |issue=7388 |pages=187–190 |date=8 March 2012 |url=http://www.physik.uni-kl.de/eggert/papers/raoul.pdf |bibcode = 2012Natur.483..187B |pmid=22398556 |arxiv=1503.06537 |s2cid=9415026 }}.

In 2014, physical experiments tested Landauer's principle and confirmed its predictions.{{Citation |author1=Yonggun Jun |author2=Momčilo Gavrilov |author3=John Bechhoefer |title=High-Precision Test of Landauer's Principle in a Feedback Trap |journal=Physical Review Letters |volume=113 |issue=19 |page=190601 |date=4 November 2014 |doi=10.1103/PhysRevLett.113.190601 |pmid=25415891 |arxiv=1408.5089 |bibcode = 2014PhRvL.113s0601J |s2cid=10164946 }}.

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 about {{convert|0.026|eV|J|abbr=on}} at 300 K, which is just 44% above the Landauer minimum.{{Cite journal |last1 = Hong |first1 = Jeongmin |last2 = Lambson |first2 = Brian |last3 = Dhuey |first3 = Scott |last4 = Bokor|author4-link=Jeffrey Bokor |first4 = Jeffrey |date = 2016-03-01 |title = Experimental test of Landauer's principle in single-bit operations on nanomagnetic memory bits |journal = Science Advances |language = en |volume = 2 |issue = 3 |pages = e1501492 |doi = 10.1126/sciadv.1501492 |issn = 2375-2548 |pmc = 4795654 |bibcode = 2016SciA....2E1492H |pmid=26998519}}.

A 2018 article published in Nature Physics features a Landauer erasure performed at cryogenic temperatures {{nobr|(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. 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.{{Citation |author1=Rocco Gaudenzi |author2=Enrique Burzuri |author3=Satoru Maegawa |author4=Herre van der Zant |author5=Fernando Luis |doi=10.1038/s41567-018-0070-7 |bibcode=2018NatPh..14..565G |title=Quantum Landauer erasure with a molecular nanomagnet |journal= Nature Physics |volume=14 |issue=6 |pages= 565–568 |date=19 March 2018 |s2cid=125321195 |url=http://resolver.tudelft.nl/uuid:c3926045-6e1a-4dd7-a584-df4a5c6b51b6 |hdl=10261/181265 |hdl-access=free }}.

Challenges

The principle is widely accepted as physical law, but it has been challenged for using circular reasoning and faulty assumptions.{{cite journal|last1=Earman |first1=John |last2=Norton |first2=John | title=Exorcist XIV: The Wrath of Maxwell's Demon. Part I. From Maxwell to Szilard| url=https://www.sciencedirect.com/science/article/pii/S1355219898000239 |access-date=2024-11-15 |date=December 1998 |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |volume=29 |issue=4 |pages=435–471 |doi=10.1016/S1355-2198(98)00023-9|bibcode=1998SHPMP..29..435E }}{{cite web |last1=Shenker |first1=Orly R. |author1-link=Orly Shenker |title=Logic and Entropy [preprint] |url=http://philsci-archive.pitt.edu/115/ |website=PhilSci Archive |access-date=20 December 2023 |archive-url=https://web.archive.org/web/20231115052855/http://philsci-archive.pitt.edu/115/ |archive-date=15 November 2023 |language=en |date=June 2000 |url-status=live}}{{cite journal |last1=Norton |first1=John D. |author1-link=John D. Norton |title=Eaters of the lotus: Landauer's principle and the return of Maxwell's demon |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |date=June 2005 |volume=36 |issue=2 |pages=375–411 |doi=10.1016/j.shpsb.2004.12.002 |bibcode=2005SHPMP..36..375N |s2cid=21104635 |url=http://philsci-archive.pitt.edu/1729/|archive-url=https://web.archive.org/web/20230605095927/http://philsci-archive.pitt.edu/1729/|archive-date=5 June 2023|url-status=live |access-date=20 December 2023 |language=en}}{{cite journal |last1=Norton |first1=John D. |author1-link=John D. Norton |title=Waiting for Landauer |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |date=August 2011 |volume=42 |issue=3 |pages=184–198 |doi=10.1016/j.shpsb.2011.05.002 |bibcode=2011SHPMP..42..184N |url=https://sites.pitt.edu/~jdnorton/papers/Waiting_SHPMP.pdf |access-date=20 December 2023 |language=en}} Others{{cite journal |last1=Ladyman |first1=James |last2=Presnell |first2=Stuart |last3=Short |first3=Anthony J. |last4=Groisman |first4=Berry |title=The connection between logical and thermodynamic irreversibility |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |date=March 2007 |volume=38 |issue=1 |pages=58–79 |doi=10.1016/j.shpsb.2006.03.007 |bibcode=2007SHPMP..38...58L |url=http://philsci-archive.pitt.edu/2689/ |access-date=20 December 2023}}{{cite journal |last1=Jordan |first1=Andrew |last2=Manikandan |first2=Sreenath |title=Some Like It Hot |journal=Inference: International Review of Science |date=12 December 2019 |volume=5 |issue=1 |doi=10.37282/991819.19.82 |s2cid=241470079 |url=https://inference-review.com/letter/some-like-it-hot |language=en}} have defended the principle, and 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.

On the other hand, recent advances in non-equilibrium statistical physics have established that there is not a prior relationship between logical and thermodynamic reversibility.{{Citation |author=Takahiro Sagawa |title= Thermodynamic and logical reversibilities revisited |journal= Journal of Statistical Mechanics: Theory and Experiment |year= 2014 |volume= 2014 |issue= 3 |page= 03025 |doi= 10.1088/1742-5468/2014/03/P03025 |arxiv= 1311.1886 |bibcode= 2014JSMTE..03..025S |s2cid= 119247579 }}. 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.{{Citation |author=David H. Wolpert |title= Stochastic thermodynamics of computation |journal= Journal of Physics A: Mathematical and Theoretical |year= 2019 |volume= 52 |issue= 19 |page= 193001 |doi= 10.1088/1751-8121/ab0850 |arxiv= 1905.05669 |bibcode= 2019JPhA...52s3001W |s2cid= 126715753 }}.

In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle,{{cite web |url=https://m.phys.org/news/2016-07-refutes-famous-physical.html |title=Computing study refutes famous claim that 'information is physical' |website=m.phys.org}} though their conclusions were disputed.{{cite journal |author=Laszlo Bela Kish |url=https://www.researchgate.net/publication/304582612 |title=Comments on 'Sub-k_BT Micro-Electromechanical Irreversible Logic Gate' |journal=Fluctuation and Noise Letters |volume=14 |number=4 |year=2016 |pages=1620001–1620194 |doi=10.1142/S0219477516200017 |accessdate=2020-03-08|arxiv=1606.09493 |bibcode=2016FNL....1520001K |s2cid=12110986 }}

References

External links

[https://noise.ece.tamu.edu/HotPI_2013/HotPI_2013.html Public debate on the validity of Landauer's principle (conference Hot Topics in Physical Informatics, November 12, 2013)]
[https://strangepaths.com/reversible-computation/2008/01/20/en/ Introductory article on Landauer's principle and reversible computing]
Maroney, O.J.E. "[https://plato.stanford.edu/entries/information-entropy/ Information Processing and Thermodynamic Entropy]" The Stanford Encyclopedia of Philosophy.
Eurekalert.org: [https://www.eurekalert.org/news-releases/706597 "Magnetic memory and logic could achieve ultimate energy efficiency"], July 1, 2011

Category:Thermodynamic entropy

Category:Entropy and information

Category:Philosophy of thermal and statistical physics

Category:Principles

Category:Limits of computation