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第1行： − {{Distinguish|Landau principle}} − 区别|兰道原理 − − '''Landauer's principle''' is a [[Principle#Principle as scientific law|physical principle]] pertaining to the lower [[Theoretical physics|theoretical]] limit of [[Energy conservation|energy consumption]] of [[computation]]. It holds that "any logically irreversible manipulation of [[Information#As a property in physics|information]], such as the erasure of a [[bit]] or the merging of two [[computation]] paths, must be accompanied by a corresponding [[entropy]] increase in non-information-bearing [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of the information-processing apparatus or its environment".<ref name = bennett>{{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 }}</ref> − − Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment". − --[[用户:Flipped| Flipped]]（[[用户讨论: Flipped |讨论]]）non-information-bearing − − --[[用户:Vicky| Vicky]]（[[用户讨论: Vicky |讨论]]）information-bearing wave 翻译为 载信息的波，所以non-information-bearing degrees of freedom 可以翻译为 非载信息自由度 − − Another way of phrasing Landauer's principle is that if an observer loses information about a [[physical system]], the observer loses the ability to extract work from that system. − − Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, the observer loses the ability to extract work from that system. − − A so-called logically-reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of [[reversible computing]]. Indeed, without reversible computing, increases in the number of computations-per-joule-of-energy-dissipated must come to a halt by about 2050: because the limit implied by Landauer's principle will be reached by then, according to [[Koomey's law]]. − − A so-called logically-reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of reversible computing. Indeed, without reversible computing, increases in the number of computations-per-joule-of-energy-dissipated must come to a halt by about 2050: because the limit implied by Landauer's principle will be reached by then, according to Koomey's law. − At 20 °C (room temperature, or 293.15 K), the Landauer limit represents an energy of approximately 0.0175 [[electron volt|eV]], or 2.805 [[zeptojoule|zJ]]. Theoretically, room{{nbhyph}}temperature computer memory operating at the Landauer limit could be changed at a rate of one billion bits per second (1Gbps) with energy being converted to heat in the memory media at the rate of only 2.805 trillionths of a watt (that is, at a rate of only 2.805 pJ/s). Modern computers use millions of times as much energy per second.<ref>{{cite web|url=http://tikalon.com/blog/blog.php?article=2011/Landauer |title=Tikalon Blog by Dev Gualtieri |publisher=Tikalon.com |date= |accessdate=May 5, 2013}}</ref><ref>{{cite web|url=http://www.bloomweb.com/nanomagnet-memories-approach-low-power-limit/ |title=Nanomagnet memories approach low-power limit | bloomfield knoble |publisher=Bloomweb.com |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}}</ref><ref>{{cite web|url=https://spectrum.ieee.org/computing/hardware/landauer-limit-demonstrated |title=Landauer Limit Demonstrated - IEEE Spectrum |publisher=Spectrum.ieee.org |date= |accessdate=May 5, 2013}}</ref> − − At 20 °C (room temperature, or 293.15 K), the Landauer limit represents an energy of approximately 0.0175 eV, or 2.805 zJ. Theoretically, roomtemperature computer memory operating at the Landauer limit could be changed at a rate of one billion bits per second (1Gbps) with energy being converted to heat in the memory media at the rate of only 2.805 trillionths of a watt (that is, at a rate of only 2.805 pJ/s). Modern computers use millions of times as much energy per second. − + − − − [[Rolf Landauer]] first proposed the principle in 1961 while working at [[IBM]].<ref name="landauer">{{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 }}</ref> 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. − − Rolf Landauer first proposed the principle in 1961 while working at IBM. 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 2011, the principle was generalized to show that while information erasure requires an increase in entropy, that increase could theoretically occur at no energy cost.<ref name="vaccaro">{{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 }}</ref> Instead, the cost can be taken in another [[Conservation law (physics)|conserved quantity]], such as [[angular momentum]]. − − In 2011, the principle was generalized to show that while information erasure requires an increase in entropy, that increase could theoretically occur at no energy cost. Instead, the cost can be taken in another conserved quantity, such as angular momentum. + − In a 2012 article published in [[Nature (journal)|''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.<ref name="berut">{{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 }}</ref> − − 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. − − 在2012年发表在[[《自然》]]杂志上的一篇文章中，来自里昂高等师范学校 École normale supérieure de Lyon、奥格斯堡大学 University of Augsburg和凯泽斯劳滕大学 University of Kaiserslautern的物理学家团队描述说，他们首次测量到了当单个数据位被擦除时释放的微小热量。 − − − In 2014, physical experiments tested Landauer's principle and confirmed its predictions.<ref name="jun">{{Citation |author1=Yonggun Jun |author2=Momčilo Gavrilov |author3=John Bechhoefer |title=High-Precision Test of Landauer's Principle in a Feedback Trap |journal=[[Phys. Rev. Lett.|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 }}</ref> − − In 2014, physical experiments tested Landauer's principle and confirmed its predictions. − − − 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 millielectron volts (4.2 [[zeptojoule]]s).<ref>{{Cite journal|last1 = Hong|first1 = Jeongmin|last2 = Lambson|first2 = Brian|last3 = Dhuey|first3 = Scott|last4 = 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}}</ref> − − 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 millielectron volts (4.2 zeptojoules). − A 2018 article published in ''[[Nature Physics]]'' features a Landauer erasure performed at cryogenic temperatures (T = 1K) on an array of high-spin (S = 10) quantum [[Single-molecule magnet|molecular magnets]]. The array is made to act as a spin register where each nanomagnet encodes a single bit of information.<ref name="Gaudenzi"></ref> 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.<ref name="Gaudenzi">{{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 }}</ref> − − A 2018 article published in Nature Physics features a Landauer erasure performed at cryogenic temperatures (T = 1K) 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. 第84行：
第37行： − + − − Landauer's principle can be understood to be a simple [[logical consequence]] of the [[second law of thermodynamics]]—which states that the entropy of an [[isolated system]] cannot decrease—together with the definition of [[thermodynamic temperature]]. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneously increase by at least a compensating amount, so that the total number of possible physical states was no smaller than it was originally (i.e. total entropy has not decreased). − − Landauer's principle can be understood to be a simple logical consequence of the second law of thermodynamics—which states that the entropy of an isolated system cannot decrease—together with the definition of thermodynamic temperature. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneously increase by at least a compensating amount, so that the total number of possible physical states was no smaller than it was originally (i.e. total entropy has not decreased). − − Yet, an increase in the number of physical states corresponding to each logical state means that, for an observer who is keeping track of the logical state of the system but not the physical state (for example an "observer" consisting of the computer itself), the number of possible physical states has increased; in other words, entropy has increased from the point of view of this observer. − − Yet, an increase in the number of physical states corresponding to each logical state means that, for an observer who is keeping track of the logical state of the system but not the physical state (for example an "observer" consisting of the computer itself), the number of possible physical states has increased; in other words, entropy has increased from the point of view of this observer. − − The maximum entropy of a bounded physical system is finite. (If the [[holographic principle]] is correct, then physical systems with finite [[surface area]] have a finite maximum entropy; but regardless of the truth of the holographic principle, [[quantum field theory]] dictates that the entropy of systems with finite radius and energy is finite due to the [[Bekenstein bound]].) To avoid reaching this maximum over the course of an extended computation, entropy must eventually be expelled to an outside environment. − − The maximum entropy of a bounded physical system is finite. (If the holographic principle is correct, then physical systems with finite surface area have a finite maximum entropy; but regardless of the truth of the holographic principle, quantum field theory dictates that the entropy of systems with finite radius and energy is finite due to the Bekenstein bound.) To avoid reaching this maximum over the course of an extended computation, entropy must eventually be expelled to an outside environment. 第110行：
第51行： − + − − Landauer's principle asserts that there is a minimum possible amount of energy required to erase one bit of information, known as the ''Landauer limit'': − − Landauer's principle asserts that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer limit: 第126行：
第63行： − − − where <math>k_\text{B}</math> is the [[Boltzmann constant]] (approximately 1.38×10<sup>−23</sup> J/K), <math>T</math> is the temperature of the heat sink in [[kelvin]]s, and <math>\ln 2</math> is the [[natural logarithm]] of 2 (approximately 0.69315). After setting ''T'' equal to room temperature 20 °C (293.15 K), we can get the Landauer limit of 0.0175 [[electron volt|eV]] (2.805 [[zeptojoule|zJ]]) per [[bit]] erased. − − where <math>k_\text{B}</math> is the Boltzmann constant (approximately 1.38×10<sup>−23</sup> J/K), <math>T</math> is the temperature of the heat sink in kelvins, and <math>\ln 2</math> is the natural logarithm of 2 (approximately 0.69315). After setting T equal to room temperature 20 °C (293.15 K), we can get the Landauer limit of 0.0175 eV (2.805 zJ) per bit erased. − − − For an environment at temperature ''T'', energy ''E'' = ''ST'' must be emitted into that environment if the amount of added entropy is ''S''. For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least ''k''<sub>B</sub> ln 2, and so, the energy that must eventually be emitted to the environment is ''E'' ≥ ''k''<sub>B</sub>''T'' ln 2. − − For an environment at temperature T, energy E = ST must be emitted into that environment if the amount of added entropy is S. For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least k<sub>B</sub> ln 2, and so, the energy that must eventually be emitted to the environment is E ≥ k<sub>B</sub>T ln 2.
无编辑摘要
本词条由11初步翻译，由Flipped完成审校。
本词条由11初步翻译，由Flipped完成审校。
'''<font color="#ff8000"> 兰道尔原理 Landauer's principle </font>'''是计算能量消耗的理论下限的物理原理。它认为，"任何逻辑上不可逆转的信息操作过程，如擦除一个比特的信息或合并两条计算路径，一定伴随着信息处理设备或其环境的非载信息自由度的相应熵的增加。"。<ref name = bennett>{{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 }}</ref>
'''<font color="#ff8000"> 兰道尔原理 Landauer's principle </font>'''是计算能量消耗的理论下限的物理原理。它认为，"任何逻辑上不可逆转的信息操作过程，如擦除一个比特的信息或合并两条计算路径，一定伴随着信息处理设备或其环境的非载信息自由度的相应熵的增加。"。<ref name = bennett>{{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 }}</ref>
兰道尔原理的另一种表述方式是，如果观察者失去了一个物理系统的信息，观察者就失去了从该系统中提取工作的能力。
兰道尔原理的另一种表述方式是，如果观察者失去了一个物理系统的信息，观察者就失去了从该系统中提取工作的能力。
所谓逻辑上可逆的计算，即不擦除任何信息，原则上可以在不释放任何热量的情况下进行。 这引起了人们对'''<font color="#ff8000"> 可逆计算 reversible computing </font>'''研究的极大兴趣。事实上，如果没有可逆计算，到2050年左右，每单位能量消耗的计算量的增加必须停止：因为根据'''<font color="#ff8000"> 库米定律 Koomey's law </font>'''，届时将达到兰道尔原理所暗示的极限。
所谓逻辑上可逆的计算，即不擦除任何信息，原则上可以在不释放任何热量的情况下进行。 这引起了人们对'''<font color="#ff8000"> 可逆计算 reversible computing </font>'''研究的极大兴趣。事实上，如果没有可逆计算，到2050年左右，每单位能量消耗的计算量的增加必须停止：因为根据'''<font color="#ff8000"> 库米定律 Koomey's law </font>'''，届时将达到兰道尔原理所暗示的极限。
在20 ° c (室温，或293.15 k)时，兰道尔极限表示大约0.0175 eV，或2.805 zJ 的能量。理论上，在兰道尔极限下工作的房间温度计算机存储器可以以每秒10亿比特(1gbps)的速度改变，能量在存储介质中以仅2.805万亿分之一瓦特的速度转化为热量(也就是说，只以2.805 pJ/s 的速度)。现代计算机每秒消耗的能量是其数百万倍。<ref>{{cite web|url=http://tikalon.com/blog/blog.php?article=2011/Landauer |title=Tikalon Blog by Dev Gualtieri |publisher=Tikalon.com |date= |accessdate=May 5, 2013}}</ref><ref>{{cite web|url=http://www.bloomweb.com/nanomagnet-memories-approach-low-power-limit/ |title=Nanomagnet memories approach low-power limit | bloomfield knoble |publisher=Bloomweb.com |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}}</ref><ref>{{cite web|url=https://spectrum.ieee.org/computing/hardware/landauer-limit-demonstrated |title=Landauer Limit Demonstrated - IEEE Spectrum |publisher=Spectrum.ieee.org |date= |accessdate=May 5, 2013}}</ref>
在20 ° c (室温，或293.15 k)时，兰道尔极限表示大约0.0175 eV，或2.805 zJ 的能量。理论上，在兰道尔极限下工作的房间温度计算机存储器可以以每秒10亿比特(1gbps)的速度改变，能量在存储介质中以仅2.805万亿分之一瓦特的速度转化为热量(也就是说，只以2.805 pJ/s 的速度)。现代计算机每秒消耗的能量是其数百万倍。<ref>{{cite web|url=http://tikalon.com/blog/blog.php?article=2011/Landauer |title=Tikalon Blog by Dev Gualtieri |publisher=Tikalon.com |date= |accessdate=May 5, 2013}}</ref><ref>{{cite web|url=http://www.bloomweb.com/nanomagnet-memories-approach-low-power-limit/ |title=Nanomagnet memories approach low-power limit | bloomfield knoble |publisher=Bloomweb.com |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}}</ref><ref>{{cite web|url=https://spectrum.ieee.org/computing/hardware/landauer-limit-demonstrated |title=Landauer Limit Demonstrated - IEEE Spectrum |publisher=Spectrum.ieee.org |date= |accessdate=May 5, 2013}}</ref>
==History 历史==
== 历史 ==
罗尔夫·兰道尔 Rolf Landauer于1961年在[[IBM]]工作时首次提出了这一原理。<ref name="landauer">{{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 }}</ref>他证明并陈述了约翰·冯·诺伊曼 John von Neumann的一个早期猜想的重要极限。因此，它有时被简单地称为兰道尔边界或兰道尔极限。
罗尔夫·兰道尔 Rolf Landauer于1961年在[[IBM]]工作时首次提出了这一原理。<ref name="landauer">{{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 }}</ref>他证明并陈述了约翰·冯·诺伊曼 John von Neumann的一个早期猜想的重要极限。因此，它有时被简单地称为兰道尔边界或兰道尔极限。
2011年，该原理被普遍化，表明信息擦除虽然需要熵的增加，但理论上这种增加可以在没有能量成本的情况下发生。<ref name="vaccaro">{{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 }}</ref>相反，成本可以用另一个'''<font color="#ff8000"> 守恒量 conserved quantity </font>'''，如'''<font color="#ff8000"> 角动量 angular momentum </font>'''来计算。
2011年，该原理被普遍化，表明信息擦除虽然需要熵的增加，但理论上这种增加可以在没有能量成本的情况下发生。<ref name="vaccaro">{{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 }}</ref>相反，成本可以用另一个'''<font color="#ff8000"> 守恒量 conserved quantity </font>'''，如'''<font color="#ff8000"> 角动量 angular momentum </font>'''来计算。
在2012年发表在[[《自然》]]杂志上的一篇文章中，来自里昂高等师范学校 École normale supérieure de Lyon、奥格斯堡大学 University of Augsburg和凯泽斯劳滕大学 University of Kaiserslautern的物理学家团队描述说，他们首次测量到了当单个数据位被擦除时释放的微小热量。<ref name="berut">{{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 }}</ref>
2014年，物理实验验证了兰道尔原理，并证实了其预测。<ref name="jun">{{Citation |author1=Yonggun Jun |author2=Momčilo Gavrilov |author3=John Bechhoefer |title=High-Precision Test of Landauer's Principle in a Feedback Trap |journal=[[Phys. Rev. Lett.|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 }}</ref>
2014年，物理实验验证了兰道尔原理，并证实了其预测。<ref name="jun">{{Citation |author1=Yonggun Jun |author2=Momčilo Gavrilov |author3=John Bechhoefer |title=High-Precision Test of Landauer's Principle in a Feedback Trap |journal=[[Phys. Rev. Lett.|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 }}</ref>
2016年，研究人员使用激光探针测量了纳米磁性位从关到开时产生的能量耗散量。翻转该磁性位需要26毫电子伏特（4.2泽普焦耳）。<ref>{{Cite journal|last1 = Hong|first1 = Jeongmin|last2 = Lambson|first2 = Brian|last3 = Dhuey|first3 = Scott|last4 = 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}}</ref>
2016年，研究人员使用激光探针测量了纳米磁性位从关到开时产生的能量耗散量。翻转该磁性位需要26毫电子伏特（4.2泽普焦耳）。<ref>{{Cite journal|last1 = Hong|first1 = Jeongmin|last2 = Lambson|first2 = Brian|last3 = Dhuey|first3 = Scott|last4 = 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}}</ref>
2018年发表在《自然物理学》上的一篇文章描述了在低温(T = 1K)下对一排高自旋(S = 10)量子'''<font color="#ff8000"> 分子磁体 molecular magnets </font>'''进行的'''<font color="#ff8000"> 兰道尔擦除 Landauer erasure </font>'''。该阵列作为自旋寄存器，每个纳米磁铁都编码一位节的信息。<ref name="Gaudenzi">{{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 }}</ref>
2018年发表在《自然物理学》上的一篇文章描述了在低温(T = 1K)下对一排高自旋(S = 10)量子'''<font color="#ff8000"> 分子磁体 molecular magnets </font>'''进行的'''<font color="#ff8000"> 兰道尔擦除 Landauer erasure </font>'''。该阵列作为自旋寄存器，每个纳米磁铁都编码一位节的信息。<ref name="Gaudenzi">{{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 }}</ref>
==Rationale 基本原理==
==基本原理==
兰道尔原理可以理解为'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics </font>'''的一个简单的逻辑后果--该定律指出，一个孤立系统的熵不能与热力学温度的定义一起减少。因为，如果计算的可能逻辑状态的数量随着计算的进行而减少(逻辑的不可逆性)，这将构成熵的被禁止的减少。除非与每个逻辑状态相应的可能物理状态的数量同时增加至少一个补偿量，从而使可能物理状态的总数不比原来少(即总熵没有减少)。
兰道尔原理可以理解为'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics </font>'''的一个简单的逻辑后果--该定律指出，一个孤立系统的熵不能与热力学温度的定义一起减少。因为，如果计算的可能逻辑状态的数量随着计算的进行而减少(逻辑的不可逆性)，这将构成熵的被禁止的减少。除非与每个逻辑状态相应的可能物理状态的数量同时增加至少一个补偿量，从而使可能物理状态的总数不比原来少(即总熵没有减少)。
然而，对系统的逻辑状态（而不是物理状态）进行跟踪的观察者(例如一个由计算机本身组成的“观察者”)来说，每个逻辑状态对应的物理状态数量的增加意味着，可能的物理状态数量增加了; 换句话说，从这个观察者的角度来看，熵增加了。
然而，对系统的逻辑状态（而不是物理状态）进行跟踪的观察者(例如一个由计算机本身组成的“观察者”)来说，每个逻辑状态对应的物理状态数量的增加意味着，可能的物理状态数量增加了; 换句话说，从这个观察者的角度来看，熵增加了。
有界物理系统的最大熵是有限的。(如果'''<font color="#ff8000"> 全息原理 holographic principle </font>'''是正确的，那么表面积有限的物理系统的最大熵是有限的; 但是不管全息原理是否正确，'''<font color="#ff8000"> 量子场理论 quantum field theory </font>'''指出，由于'''<font color="#ff8000"> 贝肯斯坦约束 Bekenstein bound </font>'''，半径和能量有限的系统的熵是有限的。）为了避免在扩展计算过程中达到这个最大值，熵最终必须被驱逐到外部环境。
有界物理系统的最大熵是有限的。(如果'''<font color="#ff8000"> 全息原理 holographic principle </font>'''是正确的，那么表面积有限的物理系统的最大熵是有限的; 但是不管全息原理是否正确，'''<font color="#ff8000"> 量子场理论 quantum field theory </font>'''指出，由于'''<font color="#ff8000"> 贝肯斯坦约束 Bekenstein bound </font>'''，半径和能量有限的系统的熵是有限的。）为了避免在扩展计算过程中达到这个最大值，熵最终必须被驱逐到外部环境。
==Equation 平衡==
==平衡==
兰道尔原理断言，擦除单位信息所需的能量是最小的，也就是著名的兰道尔极限：
兰道尔原理断言，擦除单位信息所需的能量是最小的，也就是著名的兰道尔极限：
[ math > e = k _ text { b } t ln 2
[ math > e = k _ text { b } t ln 2
其中，< math > K text { b } </math > 是'''<font color="#ff8000"> 波尔兹曼常数 Boltzmann constant </font>''' (大约1.38 × 10 < sup >-23 </sup > J/K) ，< math > T </math > 是散热器的温度，单位为开尔文，而 < math > ln 2 </math > 是2的自然对数(大约0.69315)。设 T 为室温20 ° c (293.15 k)后，可以得到擦除单位信息0.0175 eV (2.805 zJ)的兰道尔极限。
其中，< math > K text { b } </math > 是'''<font color="#ff8000"> 波尔兹曼常数 Boltzmann constant </font>''' (大约1.38 × 10 < sup >-23 </sup > J/K) ，< math > T </math > 是散热器的温度，单位为开尔文，而 < math > ln 2 </math > 是2的自然对数(大约0.69315)。设 T 为室温20 ° c (293.15 k)后，可以得到擦除单位信息0.0175 eV (2.805 zJ)的兰道尔极限。
对于温度为T的环境，如果增加的熵量为S，则必须向环境放出能量E=ST。对于丢失1位逻辑信息的计算操作，产生的熵量至少为k<sub>B</sub>ln 2，所以，最终必须向环境放出的能量为E≥k<sub>B</sub>T ln 2。
对于温度为T的环境，如果增加的熵量为S，则必须向环境放出能量E=ST。对于丢失1位逻辑信息的计算操作，产生的熵量至少为k<sub>B</sub>ln 2，所以，最终必须向环境放出的能量为E≥k<sub>B</sub>T ln 2。