“兰道尔原理”的版本间的差异

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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.  
  
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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。
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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。
  
  
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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:
  
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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。
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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：
  
  
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==Challenges==
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==Challenges 挑战==
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挑战
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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)<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>

2020年12月18日 (五) 19:23的版本

本词条由11初步翻译，由Flipped完成审校。

模板:Distinguish 区别|兰道原理

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".[1]

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 Landauer's principle 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，一定伴随着信息存储载体或其外部环境以外自由度的相应熵增加"。[1]

-- Flipped（讨论）non-information-bearing

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.

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。


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.

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 可逆计算 reversible computing 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 库米定律 Koomey's law ，届时将达到兰道尔原理所暗示的极限。


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, room模板:Nbhyphtemperature 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.[2][3][4]

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)。现代计算机每秒消耗的能量是其数百万倍。[5][6][7]


History 历史

Rolf Landauer first proposed the principle in 1961 while working at IBM.[8] 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 Rolf Landauer于1961年在IBM工作时首次提出了这一原理。[8]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。


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.[9] Instead, the cost can be taken in another 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.

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。[9]相反，成本可以用另一个 守恒量 conserved quantity ，如 角动量 angular momentum 来计算。


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.[10]

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.[11]

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

2014年，物理实验验证了兰道尔原理，并证实了其预测。[11]


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).[12]

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）。[13]


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.[14] 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.[14]

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 molecular magnets 进行的 兰道尔擦除 Landauer erasure 。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。[14]


Rationale 基本原理

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).

兰道尔原理可以理解为 热力学第二定律 second law of thermodynamics 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)。


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，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。


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 holographic principle 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， 量子场理论 quantum field theory 指出，由于 贝肯斯坦约束 Bekenstein bound ，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

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，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]\displaystyle{ E = k_\text{B} T \ln 2 }[/math]

[math]\displaystyle{ E = k_\text{B} T \ln 2 }[/math]

[ math > e = k _ text { b } t ln 2


where [math]\displaystyle{ k_\text{B} }[/math] is the Boltzmann constant (approximately 1.38×10−23 J/K), [math]\displaystyle{ T }[/math] is the temperature of the heat sink in kelvins, and [math]\displaystyle{ \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.

where [math]\displaystyle{ k_\text{B} }[/math] is the Boltzmann constant (approximately 1.38×10−23 J/K), [math]\displaystyle{ T }[/math] is the temperature of the heat sink in kelvins, and [math]\displaystyle{ \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，< math > K text { b } </math > 是 波尔兹曼常数 Boltzmann constant (大约1.38 × 10 < sup >-23 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。


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 kB ln 2, and so, the energy that must eventually be emitted to the environment is E ≥ kBT 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 kB ln 2, and so, the energy that must eventually be emitted to the environment is E ≥ kBT 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kBln 2，所以，最终必须向环境放出的能量为E≥kBT ln 2。


Challenges 挑战

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)[15] and Norton (2004,[16] 2011[17]), and defended by Bennett (2003),[1] Ladyman et al. (2007),[18] and by Jordan and Manikandan (2019).[19]

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).

这一原理被广泛接受为物理定律，但近年来，它因使用 循环推理 circular reasoning 和错误假设而受到挑战，尤其是厄尔曼 Earman和诺顿 Norton (1998年) ，是申克 shenker (2000年) [15]和Norton (2004年)</ref> 2011[17]) ，在这之后，贝内特 bennett (2003年[1])，约旦 Ladyman（2007年[18]）和马尼坎达 Manikandan (2019年[19])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.[20] 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.[21]

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已经确定，逻辑可逆性和热力学可逆性之间不存在先验关系。[20]一个物理过程有可能在逻辑上是可逆的，但在热力学上是不可逆的。也有可能一个物理过程在逻辑上是不可逆的，但在热力学上是可逆的。用逻辑上可逆的系统进行计算的好处极其微小。[21]


In 2016, researchers at the University of Perugia claimed to have demonstrated a violation of Landauer’s principle.[22] However, according to Laszlo Kish (2016),[23] 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 University of Perugia的研究人员声称已经证明违反了兰道尔原理。[24]然而，根据拉斯洛·基什 Laszlo Kish (2016) ，[25]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

请参阅

玛格罗斯·莱维汀定理

布雷曼极限

贝肯斯坦约束

科尔莫戈罗夫复杂性

热力学和信息理论中的熵

信息理论

贾任斯基恒等式


计算限制

扩展思维理论

麦克斯韦妖

库米定律


References

参考

  1. ↑ 1.0 1.1 1.2 1.3 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. ↑ "Tikalon Blog by Dev Gualtieri". Tikalon.com. Retrieved May 5, 2013.
  3. ↑ "Nanomagnet memories approach low-power limit | bloomfield knoble". Bloomweb.com. Archived from the original on December 19, 2014. Retrieved May 5, 2013.
  4. ↑ "Landauer Limit Demonstrated - IEEE Spectrum". Spectrum.ieee.org. Retrieved May 5, 2013.
  5. ↑ "Tikalon Blog by Dev Gualtieri". Tikalon.com. Retrieved May 5, 2013.
  6. ↑ "Nanomagnet memories approach low-power limit | bloomfield knoble". Bloomweb.com. Archived from the original on December 19, 2014. Retrieved May 5, 2013.
  7. ↑ "Landauer Limit Demonstrated - IEEE Spectrum". Spectrum.ieee.org. Retrieved May 5, 2013.
  8. ↑ 8.0 8.1 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
  9. ↑ 9.0 9.1 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
  10. ↑ 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
  11. ↑ 11.0 11.1 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
  12. ↑ 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 (in English). 2 (3): e1501492. Bibcode:2016SciA....2E1492H. doi:10.1126/sciadv.1501492. ISSN 2375-2548. PMC 4795654. PMID 26998519.
  13. ↑ 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 (in English). 2 (3): e1501492. Bibcode:2016SciA....2E1492H. doi:10.1126/sciadv.1501492. ISSN 2375-2548. PMC 4795654. PMID 26998519.
  14. ↑ 14.0 14.1 14.2 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, S2CID 125321195
  15. ↑ 15.0 15.1 Logic and Entropy Critique by Orly Shenker (2000)
  16. ↑ Eaters of the Lotus Critique by John Norton (2004)
  17. ↑ 17.0 17.1 Waiting for Landauer Response by Norton (2011) 引用错误：无效<ref>标签；name属性“norton2”使用不同内容定义了多次
  18. ↑ 18.0 18.1 The Connection between Logical and Thermodynamic Irreversibility Defense by Ladyman et al. (2007)
  19. ↑ 19.0 19.1 Some Like It Hot, Letter to the Editor in reply to Norton's article by A. Jordan and S. Manikandan (2019)
  20. ↑ 20.0 20.1 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
  21. ↑ 21.0 21.1 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
  22. ↑ "Computing study refutes famous claim that 'information is physical'". m.phys.org.
  23. ↑ Laszlo Bela Kish42.27Texas A&M University. "Comments on "Sub-kBT Micro-Electromechanical Irreversible Logic Gate"". Retrieved 2020-03-08.{{cite web}}: CS1 maint: multiple names: authors list (link)
  24. ↑ "Computing study refutes famous claim that 'information is physical'". m.phys.org.
  25. ↑ Laszlo Bela Kish42.27Texas A&M University. "Comments on "Sub-kBT Micro-Electromechanical Irreversible Logic Gate"". Retrieved 2020-03-08.{{cite web}}: CS1 maint: multiple names: authors list (link)


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Category:Thermodynamic entropy

类别: 热力学熵

Category:Entropy and information

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