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Moved page from wikipedia:en:Landauer's principle (history)
此词条暂由彩云小译翻译，翻译字数共1031，未经人工整理和审校，带来阅读不便，请见谅。
{{Distinguish|Landau principle}}
'''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".
兰道尔原理是关于计算能量消耗的理论下限的一个物理原理。它认为，”任何逻辑上不可逆的信息操作，例如位的擦除或两个计算路径的合并，必须伴随着信息处理设备或其环境的非信息承载自由度的相应熵增加”。
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.
另一种表述兰道尔原理的方式是，如果一个观察者丢失了有关物理系统的信息，那么这个观察者就失去了从该系统中提取工作的能力。
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.
一个所谓的逻辑可逆计算，其中没有信息擦除，原则上可以进行不释放任何热量。这使得人们对可逆计算的研究产生了浓厚的兴趣。事实上，如果没有可逆计算，到2050年左右，耗散的计算数量——每焦耳的能量——的增加必须停止: 因为根据 Koomey 定律，到那时，Landauer 原理所暗示的极限将达到。
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.
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)。现代计算机每秒钟要消耗数百万倍的能量。
==History==
[[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.
罗尔夫 · 兰道尔于1961年在 IBM 工作时首次提出了这一原则。他证明并陈述了早期约翰·冯·诺伊曼的一个猜想的重要限度。由于这个原因，它有时被简单地称为兰道尔极限或兰道尔极限。
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.
在2011年，这个原理被推广到表明，虽然消除信息需要增加熵，但理论上这种增加可以在没有能源成本的情况下发生。相反，成本可以在另一个守恆量承担，比如角动量。
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、奥格斯堡大学和 Kaiserslautern 大学的一组物理学家描述说，他们首次测量了单个数据被擦除时释放的微量热量。
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.
2014年，物理实验验证了兰道尔的原理，并证实了其预测。
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).
2016年，研究人员使用激光探测器测量了纳米磁位从关闭到打开时所产生的能量耗散量。翻转钻头需要26毫电子伏(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.
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)量子分子磁体进行的兰道尔擦除(Landauer erasure)。该阵列作为一个自旋寄存器，每个纳米粒子网编码一位信息。
==Rationale==
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).
的原理可以理解为热力学第二定律的一个简单蕴涵---- 该定律指出孤立系统的熵不能减少---- 与热力学温度的定义一起。因为，如果一个计算的可能逻辑状态的数量随着计算的进行而减少(逻辑不可逆性) ，这将构成熵的禁止减少，除非每个逻辑状态对应的可能物理状态的数量同时增加至少一个补偿量，以使可能的物理状态的总数不小于原来的数量(即:。总熵没有减少)。
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.
然而，每个逻辑状态对应的物理状态数量的增加意味着，对于一个跟踪系统的逻辑状态而不是物理状态的观察者(例如一个由计算机本身组成的“观察者”)来说，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。
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.
有界物理系统的最大熵是有限的。(如果全息原理理论是正确的，那么有限表面积的物理系统有一个有限的最大熵; 但是不管全息原理理论是否正确，量子场理论指出，有限半径和能量的系统的熵是有限的，这是由于贝肯斯坦上限的存在。)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中。
==Equation==
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:
兰道尔原理断言，删除一点信息所需要的能量是最小的，这就是兰道尔极限:
:<math>E = k_\text{B} T \ln 2</math>
<math>E = k_\text{B} T \ln 2</math>
[ math > e = k _ text { b } t ln 2
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.
其中，k text { b } </math > 是波兹曼常数(大约1.38 × 10 < sup >-23 </sup > J/K) ，t </math > 是科尔文散热器的温度，而 < math > ln 2 </math > 是2的自然对数(大约0.69315)。设置 t 为室温20 ° c (293.15 k)后，可以得到每位擦除0.0175 eV (2.805 zJ)的朗道尔极限。
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.
对于一个温度为 t 的环境，如果附加熵的量为 s，则能量 e = ST 必须被发射到该环境中。对于一个计算操作，其中丢失了1位逻辑信息，所产生的熵至少为 k < sub > b </sub > ln & # 8239; 2，因此，最终发射到环境中的能量为 e ≥ k < sub > b </sub > t ln & # 8239; 2。
==Challenges==
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)<ref name="shenker">[http://philsci-archive.pitt.edu/archive/00000115/ Logic and Entropy] Critique by Orly Shenker (2000)</ref> and Norton (2004,<ref name="norton">[http://philsci-archive.pitt.edu/archive/00001729/ Eaters of the Lotus] Critique by John Norton (2004)</ref> 2011<ref name="norton2">[http://www.pitt.edu/~jdnorton/papers/Waiting_SHPMP.pdf Waiting for Landauer] Response by Norton (2011)</ref>), and defended by Bennett (2003),<ref name="bennett" /> Ladyman et al. (2007),<ref name="short">[http://philsci-archive.pitt.edu/archive/00002689/ The Connection between Logical and Thermodynamic Irreversibility] Defense by Ladyman et al. (2007)</ref> and by Jordan and Manikandan (2019).<ref name="jordan">[https://inference-review.com/letter/some-like-it-hot Some Like It Hot], Letter to the Editor in reply to Norton's article by A. Jordan and S. Manikandan (2019)</ref>
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) and Norton (2004, 2011), and defended by Bennett (2003), and by Jordan and Manikandan (2019).
这一原则被广泛接受为物理定律，但近年来，它因使用循环推理和错误假设而受到挑战，尤其是在厄尔曼和诺顿(1998年) ，随后在申克(2000年)和诺顿(2004年，2011年) ，贝内特(2003年)和约旦和马尼坎达(2019年)为之辩护。
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.<ref name="sagawa">{{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 }}</ref> 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 systems are nuanced.<ref name="wolpert">{{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 }}</ref>
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. 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 systems are nuanced.
另一方面，非平衡统计物理学的最新进展表明，逻辑可逆性和热力学可逆性之间不存在先验关系。物理过程在逻辑上是可逆的，但在热力学上是不可逆的，这是可能的。物理过程在逻辑上是不可逆的，但在热力学上是可逆的，这也是可能的。充其量，使用逻辑可逆的系统实现计算的好处是微妙的。
In 2016, researchers at the [[University of Perugia]] claimed to have demonstrated a violation of Landauer’s principle.<ref>{{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}}</ref> However, according to Laszlo Kish (2016),<ref>{{cite web|author=Laszlo Bela Kish42.27Texas A&M University |url=https://www.researchgate.net/publication/304582612 |title=Comments on "Sub-kBT Micro-Electromechanical Irreversible Logic Gate" |date= |accessdate=2020-03-08}}</ref> their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode".
In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle. However, according to Laszlo Kish (2016), their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode".
2016年，佩鲁贾大学的研究人员声称已经证明了对兰道尔原理的违反。然而，根据 Laszlo Kish (2016) ，他们的结果是无效的，因为他们“忽略了能量耗散的主要来源，即输入电极电容的充电能量”。
==See also==
* [[Margolus–Levitin theorem]]
* [[Bremermann's limit]]
* [[Bekenstein bound]]
* [[Kolmogorov complexity]]
* [[Entropy in thermodynamics and information theory]]
* [[Information theory]]
* [[Jarzynski equality]]
* [[Limits to computation]]
* [[Extended mind thesis]]
* [[Maxwell's demon]]
*[[Koomey's law|Koomey's Law]]
==References==
{{reflist}}
==Further reading==
*{{citation| author1-first= Mikhail | author1-last= Prokopenko | author2-first=Joseph T. | author2-last= Lizier | title= Transfer entropy and transient limits of computation | journal= [[Scientific Reports]] | date= 2014 | volume=4 | page= 5394 | doi= 10.1038/srep05394| pmid= 24953547 | bibcode= 2014NatSR...4E5394P | pmc= 4066251 }}
==External links==
{{Library resources box}}
* [http://www.ece.tamu.edu/~noise/HotPI_2013/HotPI_2013.html Public debate on the validity of Landauer's principle (conference Hot Topics in Physical Informatics, November 12, 2013)]
* [http://strangepaths.com/reversible-computation/2008/01/20/en/ Introductory article on Landauer's principle and reversible computing]
* Maroney, O.J.E. "[http://plato.stanford.edu/entries/information-entropy/ Information Processing and Thermodynamic Entropy]" The Stanford Encyclopedia of Philosophy.
* Eurekalert.org: [http://www.eurekalert.org/pub_releases/2011-07/uoc--mma063011.php "Magnetic memory and logic could achieve ultimate energy efficiency"], July 1, 2011
{{Authority control}}
[[Category:Thermodynamic entropy]]
Category:Thermodynamic entropy
类别: 熵
[[Category:Entropy and information]]
Category:Entropy and information
类别: 熵和信息
[[Category:Philosophy of thermal and statistical physics]]
Category:Philosophy of thermal and statistical physics
类别: 热力学和统计物理学哲学
[[Category:Principles]]
Category:Principles
类别: 原则
[[Category:Limits of computation]]
Category:Limits of computation
类别: 计算限制
<noinclude>
<small>This page was moved from [[wikipedia:en:Landauer's principle]]. Its edit history can be viewed at [[兰道尔原理/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{Distinguish|Landau principle}}
'''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".
兰道尔原理是关于计算能量消耗的理论下限的一个物理原理。它认为，”任何逻辑上不可逆的信息操作，例如位的擦除或两个计算路径的合并，必须伴随着信息处理设备或其环境的非信息承载自由度的相应熵增加”。
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.
另一种表述兰道尔原理的方式是，如果一个观察者丢失了有关物理系统的信息，那么这个观察者就失去了从该系统中提取工作的能力。
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.
一个所谓的逻辑可逆计算，其中没有信息擦除，原则上可以进行不释放任何热量。这使得人们对可逆计算的研究产生了浓厚的兴趣。事实上，如果没有可逆计算，到2050年左右，耗散的计算数量——每焦耳的能量——的增加必须停止: 因为根据 Koomey 定律，到那时，Landauer 原理所暗示的极限将达到。
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.
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)。现代计算机每秒钟要消耗数百万倍的能量。
==History==
[[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.
罗尔夫 · 兰道尔于1961年在 IBM 工作时首次提出了这一原则。他证明并陈述了早期约翰·冯·诺伊曼的一个猜想的重要限度。由于这个原因，它有时被简单地称为兰道尔极限或兰道尔极限。
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.
在2011年，这个原理被推广到表明，虽然消除信息需要增加熵，但理论上这种增加可以在没有能源成本的情况下发生。相反，成本可以在另一个守恆量承担，比如角动量。
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、奥格斯堡大学和 Kaiserslautern 大学的一组物理学家描述说，他们首次测量了单个数据被擦除时释放的微量热量。
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.
2014年，物理实验验证了兰道尔的原理，并证实了其预测。
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).
2016年，研究人员使用激光探测器测量了纳米磁位从关闭到打开时所产生的能量耗散量。翻转钻头需要26毫电子伏(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.
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)量子分子磁体进行的兰道尔擦除(Landauer erasure)。该阵列作为一个自旋寄存器，每个纳米粒子网编码一位信息。
==Rationale==
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).
的原理可以理解为热力学第二定律的一个简单蕴涵---- 该定律指出孤立系统的熵不能减少---- 与热力学温度的定义一起。因为，如果一个计算的可能逻辑状态的数量随着计算的进行而减少(逻辑不可逆性) ，这将构成熵的禁止减少，除非每个逻辑状态对应的可能物理状态的数量同时增加至少一个补偿量，以使可能的物理状态的总数不小于原来的数量(即:。总熵没有减少)。
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.
然而，每个逻辑状态对应的物理状态数量的增加意味着，对于一个跟踪系统的逻辑状态而不是物理状态的观察者(例如一个由计算机本身组成的“观察者”)来说，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。
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.
有界物理系统的最大熵是有限的。(如果全息原理理论是正确的，那么有限表面积的物理系统有一个有限的最大熵; 但是不管全息原理理论是否正确，量子场理论指出，有限半径和能量的系统的熵是有限的，这是由于贝肯斯坦上限的存在。)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中。
==Equation==
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:
兰道尔原理断言，删除一点信息所需要的能量是最小的，这就是兰道尔极限:
:<math>E = k_\text{B} T \ln 2</math>
<math>E = k_\text{B} T \ln 2</math>
[ math > e = k _ text { b } t ln 2
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.
其中，k text { b } </math > 是波兹曼常数(大约1.38 × 10 < sup >-23 </sup > J/K) ，t </math > 是科尔文散热器的温度，而 < math > ln 2 </math > 是2的自然对数(大约0.69315)。设置 t 为室温20 ° c (293.15 k)后，可以得到每位擦除0.0175 eV (2.805 zJ)的朗道尔极限。
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.
对于一个温度为 t 的环境，如果附加熵的量为 s，则能量 e = ST 必须被发射到该环境中。对于一个计算操作，其中丢失了1位逻辑信息，所产生的熵至少为 k < sub > b </sub > ln & # 8239; 2，因此，最终发射到环境中的能量为 e ≥ k < sub > b </sub > t ln & # 8239; 2。
==Challenges==
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)<ref name="shenker">[http://philsci-archive.pitt.edu/archive/00000115/ Logic and Entropy] Critique by Orly Shenker (2000)</ref> and Norton (2004,<ref name="norton">[http://philsci-archive.pitt.edu/archive/00001729/ Eaters of the Lotus] Critique by John Norton (2004)</ref> 2011<ref name="norton2">[http://www.pitt.edu/~jdnorton/papers/Waiting_SHPMP.pdf Waiting for Landauer] Response by Norton (2011)</ref>), and defended by Bennett (2003),<ref name="bennett" /> Ladyman et al. (2007),<ref name="short">[http://philsci-archive.pitt.edu/archive/00002689/ The Connection between Logical and Thermodynamic Irreversibility] Defense by Ladyman et al. (2007)</ref> and by Jordan and Manikandan (2019).<ref name="jordan">[https://inference-review.com/letter/some-like-it-hot Some Like It Hot], Letter to the Editor in reply to Norton's article by A. Jordan and S. Manikandan (2019)</ref>
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) and Norton (2004, 2011), and defended by Bennett (2003), and by Jordan and Manikandan (2019).
这一原则被广泛接受为物理定律，但近年来，它因使用循环推理和错误假设而受到挑战，尤其是在厄尔曼和诺顿(1998年) ，随后在申克(2000年)和诺顿(2004年，2011年) ，贝内特(2003年)和约旦和马尼坎达(2019年)为之辩护。
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.<ref name="sagawa">{{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 }}</ref> 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 systems are nuanced.<ref name="wolpert">{{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 }}</ref>
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. 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 systems are nuanced.
另一方面，非平衡统计物理学的最新进展表明，逻辑可逆性和热力学可逆性之间不存在先验关系。物理过程在逻辑上是可逆的，但在热力学上是不可逆的，这是可能的。物理过程在逻辑上是不可逆的，但在热力学上是可逆的，这也是可能的。充其量，使用逻辑可逆的系统实现计算的好处是微妙的。
In 2016, researchers at the [[University of Perugia]] claimed to have demonstrated a violation of Landauer’s principle.<ref>{{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}}</ref> However, according to Laszlo Kish (2016),<ref>{{cite web|author=Laszlo Bela Kish42.27Texas A&M University |url=https://www.researchgate.net/publication/304582612 |title=Comments on "Sub-kBT Micro-Electromechanical Irreversible Logic Gate" |date= |accessdate=2020-03-08}}</ref> their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode".
In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle. However, according to Laszlo Kish (2016), their results are invalid because they "neglect the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode".
2016年，佩鲁贾大学的研究人员声称已经证明了对兰道尔原理的违反。然而，根据 Laszlo Kish (2016) ，他们的结果是无效的，因为他们“忽略了能量耗散的主要来源，即输入电极电容的充电能量”。
==See also==
* [[Margolus–Levitin theorem]]
* [[Bremermann's limit]]
* [[Bekenstein bound]]
* [[Kolmogorov complexity]]
* [[Entropy in thermodynamics and information theory]]
* [[Information theory]]
* [[Jarzynski equality]]
* [[Limits to computation]]
* [[Extended mind thesis]]
* [[Maxwell's demon]]
*[[Koomey's law|Koomey's Law]]
==References==
{{reflist}}
==Further reading==
*{{citation| author1-first= Mikhail | author1-last= Prokopenko | author2-first=Joseph T. | author2-last= Lizier | title= Transfer entropy and transient limits of computation | journal= [[Scientific Reports]] | date= 2014 | volume=4 | page= 5394 | doi= 10.1038/srep05394| pmid= 24953547 | bibcode= 2014NatSR...4E5394P | pmc= 4066251 }}
==External links==
{{Library resources box}}
* [http://www.ece.tamu.edu/~noise/HotPI_2013/HotPI_2013.html Public debate on the validity of Landauer's principle (conference Hot Topics in Physical Informatics, November 12, 2013)]
* [http://strangepaths.com/reversible-computation/2008/01/20/en/ Introductory article on Landauer's principle and reversible computing]
* Maroney, O.J.E. "[http://plato.stanford.edu/entries/information-entropy/ Information Processing and Thermodynamic Entropy]" The Stanford Encyclopedia of Philosophy.
* Eurekalert.org: [http://www.eurekalert.org/pub_releases/2011-07/uoc--mma063011.php "Magnetic memory and logic could achieve ultimate energy efficiency"], July 1, 2011
{{Authority control}}
[[Category:Thermodynamic entropy]]
Category:Thermodynamic entropy
类别: 熵
[[Category:Entropy and information]]
Category:Entropy and information
类别: 熵和信息
[[Category:Philosophy of thermal and statistical physics]]
Category:Philosophy of thermal and statistical physics
类别: 热力学和统计物理学哲学
[[Category:Principles]]
Category:Principles
类别: 原则
[[Category:Limits of computation]]
Category:Limits of computation
类别: 计算限制
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<small>This page was moved from [[wikipedia:en:Landauer's principle]]. Its edit history can be viewed at [[兰道尔原理/edithistory]]</small></noinclude>
[[Category:待整理页面]]