内容来源：https://www.quantamagazine.org/a-thermometer-for-measuring-quantumness-20251001/

内容总结：

【科技前沿】科学家开发“量子性测温计” 热力学定律揭示量子世界新奥秘

热力学第二定律指出热量会自发从高温物体流向低温物体，这一经典理论正被量子物理研究重新诠释。巴西物理学家亚历山德雷·德奥利维拉与丹麦技术大学团队近日发现，在量子尺度下热量可能逆向流动，这种现象竟可成为探测“量子性”的全新工具。

量子世界存在两种特殊状态：叠加态（量子系统同时处于多种状态）和纠缠态（多个量子系统状态相互关联）。传统观测方式会破坏这些脆弱状态，而新方法通过监测热量流动即可实现无损探测。研究团队构建了一个包含量子系统、信息存储单元和散热器的三重结构，当系统存在量子纠缠时，散热器吸收的热量将超越经典物理极限，通过读取散热器温度变化就能反推量子系统的纠缠特性。

这项研究揭示了热力学与信息论的深刻联系。早在19世纪，物理学家麦克斯韦就曾提出“麦克斯韦妖”的思想实验，探讨信息如何影响热力学系统。最新研究证明，量子纠缠所承载的互信息可以成为热力学资源，通过消耗量子关联来驱动逆向热流，这种“量子制冷”过程本质上并未违背热力学第二定律。

该技术有望应用于量子计算机验证。牛津大学物理学家弗拉特科·韦德拉尔指出，当前量子计算设备常面临“是否真正利用量子资源”的质疑，新方法可通过简单测量散热器能量变化给出答案。研究团队正与巴西圣保罗联邦大学实验组合作，利用氯仿分子中碳氢原子的自旋状态进行原理验证。

更令人振奋的是，这种方法或将为探索引力量子化提供新路径。若两个物体仅通过引力相互作用产生纠缠，通过热力学测量即可捕捉这种关联，从而验证引力是否具有量子特性。韦德拉尔表示：“用如此直观的宏观测量解答物理学深层问题，将是极具魅力的突破。”

（根据《量子杂志》报道整理）

中文翻译：

测量“量子性”的温度计

引言
若说哪条物理定律最易于理解，热力学第二定律当仁不让：热量会自发从高温物体流向低温物体。但在哥本哈根的一家咖啡馆里，巴西物理学家小亚历山德雷·德奥利维拉用温和而不经意的方式让我意识到，自己从未真正理解这条定律。

“您看这杯热咖啡和这壶冰牛奶，”这位物理学家说道。当两者接触时，热量确实会如德国科学家鲁道夫·克劳修斯于1850年首次明确阐述的那样，从高温物体流向低温物体。但德奥利维拉解释道，物理学家们发现，在某些情况下量子力学定律会驱使热量逆向流动——从低温物体传向高温物体。

他补充道，这并非意味着第二定律失效。随着咖啡逐渐冷却，他从容指出：克劳修斯的表述只是量子物理要求的更完整公式的“经典近似”。

二十多年前物理学家开始意识到这一精妙之处，此后便持续探索第二定律的量子力学版本。如今，丹麦技术大学博士后研究员德奥利维拉与同事证明，量子尺度下的“反常热流”具有巧妙用途。

他们提出，这种方法可便捷探测“量子性”——例如感知物体处于多种可能观测状态的量子“叠加态”，或确认两个物体处于状态相互依存的“纠缠态”——且不破坏这些脆弱的量子现象。该诊断工具能确保量子计算机真正运用量子资源进行计算，甚至可能助力探测引力的量子特性，这是现代物理学的远期目标之一。研究人员表示，只需将量子系统与能存储其信息的第二系统及散热装置（能吸收大量能量的物体）相连，即可突破经典物理允许的极限，增强向散热装置的热量传递。通过测量散热装置的温度变化，就能探测量子系统中的叠加或纠缠现象。

抛开实用价值，这项研究揭示了热力学深层原理的新维度：物理系统中热量与能量的转化转移，与系统本身的信息（即可知或未知的特性）密切相关。在此过程中，我们通过牺牲量子系统的存储信息来“换取”反常热流。

“我欣赏这种用热力学量表征量子现象的思路，”马里兰大学物理学家妮可·容格·哈尔彭表示，“这个课题既基础又深刻。”

知即为能

热力学第二定律与信息的关联最早由苏格兰物理学家詹姆斯·克拉克·麦克斯韦在19世纪探索。令他不安的是，克劳修斯的第二定律似乎暗示宇宙中的热量终将消散，直至所有温差消失。在此过程中，宇宙总熵（粗略衡量无序程度的指标）将不可逆转地增加。麦克斯韦意识到，这种趋势最终将剥夺利用热流做功的可能性，宇宙会陷入热运动均匀嗡鸣的死寂平衡——“热寂”。这个预言足以令任何人不安，对虔诚的基督徒麦克斯韦更是如此。但在1867年致友人彼得·格思里·泰特的信中，他宣称找到了第二定律的“漏洞”。

他设想了一个能观察气体分子运动的微小生灵（后被称为“麦克斯韦妖”）。气体充满被带活隔板隔成两半的容器，通过选择性开合隔板，妖能将快速分子与慢速分子分离，形成高温与低温气体。借助分子运动信息，妖降低了气体熵值，创造出可驱动活塞做功的温度梯度。

科学家们确信麦克斯韦妖无法真正违背第二定律，但耗费近百年才揭示原因：妖收集存储的分子运动信息终将占满其有限内存，必须擦除重置才能继续工作。物理学家罗尔夫·兰道尔于1961年证明，这种擦除操作会消耗能量并产生熵增——其数值超过妖分拣分子所减少的熵。兰道尔的分析建立了信息与熵的等价关系，意味着信息本身可作为热力学资源转化为功。2010年，物理学家通过实验验证了信息到能量的转化。

但量子现象允许以经典物理禁止的方式处理信息——这正是量子计算与量子加密等技术的基础，也是量子理论颠覆传统第二定律的原因。

开发关联性

纠缠的量子物体具有互信息：它们相互关联，通过观察一方可知另一方特性。这本身并不奇特——若发现一只手套是左撇，便知另一只是右撇。但纠缠量子粒子对与手套存在本质区别：手套的左右性在观察前已确定，而根据量子力学，粒子在测量前其可观测属性值并未确定。此时我们仅能知晓可能取值组合的概率（例如50%左-右与50%右-左）。唯有测量其中一个粒子状态时，这些可能性才坍缩为确定结果——在此过程中纠缠态被破坏。

若气体分子以此方式纠缠，麦克斯韦妖就能更高效地操控它们。例如，当妖知道观测到的快速分子与紧随其后的另一个快速分子存在关联时，就无需费心观察第二个粒子即可打开隔板放行。（暂时）规避第二定律的热力学代价由此降低。

2004年，维也纳大学的卡斯拉夫·布鲁克纳与当时任职于伦敦帝国学院的弗拉特科·韦德拉尔指出，这意味着宏观热力学测量可作为“见证者”揭示粒子间的量子纠缠。他们证明，在某些条件下，系统的热容量或对外磁场的响应会留下纠缠态的印记。

类似地，其他物理学家计算出：当系统中存在量子纠缠时，从温热物体中提取的功将超过纯经典系统。

2008年，加州州立大学的物理学家霍塞因·帕托维揭示了量子纠缠颠覆经典热力学预想的惊人推论：纠缠的存在实际上能逆转热量从高温物体向低温物体的自发流动，看似推翻了第二定律本身。

哈尔彭指出，这种逆转是特殊的制冷过程。与常规制冷相同，它并非无偿（故未真正破坏第二定律）。经典情况下制冷需要做功：通过消耗燃料使热量“逆向”流动，补偿因冷却低温物体、加热高温物体损失的熵。但在量子情形中，哈尔彭说：“你消耗的是关联性而非燃料。”换言之，随着反常热流进行，纠缠态被破坏——初始具有关联特性的粒子变得独立。“我们可以利用关联性作为推动热量逆向流动的资源，”她解释道。

本质上，这里的燃料就是信息本身——具体而言是纠缠态冷热物体间的互信息。

两年后，伦敦帝国学院的大卫·詹宁斯与特里·鲁道夫阐明了机制。他们提出了包含互信息情形的热力学第二定律新表述，并计算出量子关联消耗改变乃至逆转经典热流的极限。

妖之知

当量子效应介入时，第二定律不再简单。我们能否利用量子物理放宽热力学定律约束的方式做些有用之事？这正是量子热力学学科的目标之一——有些研究者试图制造效率超越经典引擎的量子引擎，或充电更快的量子电池。

波兰科学院理论物理中心的帕特里克·利普卡-巴尔托西奇则反向探索实际应用：利用热力学作为探测量子物理的工具。去年，他与同事实现了布鲁克纳和韦德拉尔2004年的设想——用热力学性质作为量子纠缠的见证者。他们的方案包含相互关联的冷热量子系统，以及介导两者间热流的第三系统。这个第三系统可视为麦克斯韦妖，但其拥有可与受操控系统纠缠的“量子记忆”。与妖的记忆纠缠有效连接了冷热系统，使妖能通过一方特性推断另一方信息。

这种量子妖可作为催化剂，通过访问其他方式无法获取的关联性促进热传递。由于与冷热物体纠缠，妖能系统性地洞察并利用所有关联。且如催化剂般，该第三系统在物体间热交换完成后恢复初始状态。这种方式能使反常热流突破无催化剂时的极限。

德奥利维拉今年与利普卡-巴尔托西奇、丹麦技术大学的约纳坦·玻尔·布拉斯克合著的论文运用了类似理念，但关键差异使其成为测量量子性的温度计。早期研究中，类妖量子记忆与一对相互关联的冷热量子系统相互作用；而新研究中，它位于量子系统（如量子计算机中的纠缠量子比特阵列）与未直接纠缠的简单散热装置之间。

由于记忆同时与量子系统及散热装置纠缠，它仍能催化超越经典极限的热流。在此过程中，量子系统内的纠缠态转化为额外热量进入散热装置。因此测量散热装置储存的能量（类似读取“温度”）即可揭示量子系统中的纠缠现象。由于系统与散热装置本身未纠缠，测量不影响量子系统状态。这一策略规避了测量破坏量子性的经典难题。“若直接对量子系统进行测量，纠缠态在过程展开前就会被破坏，”德奥利维拉指出。

现任牛津大学的韦德拉尔认为，新方案兼具简洁性与普适性。“这类验证协议非常重要，”他表示：每当量子计算机公司宣布其最新设备性能时，如何（或是否）真正确认量子比特间的纠缠助力计算始终是关键问题。散热装置仅通过能量变化即可作为此类量子现象的探测器。为实现该设想，可指定一个量子比特作为记忆单元（其状态反映其他量子比特状态），再将此记忆量子比特耦合至作为散热装置的粒子群（其能量可被测量）。韦德拉尔补充，前提是需要对系统实现精确控制以确保无其他热源干扰测量，且该方法无法检测所有纠缠态。

德奥利维拉认为现有系统已可实验验证他们的想法。他与同事正与巴西圣保罗联邦ABC大学的罗伯托·塞拉研究组讨论该目标。2016年，塞拉团队曾利用氯仿分子中碳氢原子的磁取向（自旋）作为量子比特实现热传递。

德奥利维拉表示，利用该装置应能通过量子行为（此处指相干性，即两个及以上自旋属性同步演化）改变原子间热流。量子比特相干性对量子计算至关重要，通过探测反常热交换予以验证将大有裨益。

意义远不止于此。多个研究组正尝试设计实验验证引力是否如其他三种基本力般具有量子性。部分方案涉及探测纯粹由引力相互作用产生的两物体间量子纠缠。或许研究者能通过对物体进行简易热力学测量，探查这类引力诱导的纠缠——从而验证（或否定）引力的量子化本质。

韦德拉尔感叹：“若能通过如此简易宏观的方式探究物理学最深奥的问题，岂非美事一桩？”

英文来源：

A Thermometer for Measuring Quantumness
Introduction
If there’s one law of physics that seems easy to grasp, it’s the second law of thermodynamics: Heat flows spontaneously from hotter bodies to colder ones. But now, gently and almost casually, Alexssandre de Oliveira Jr. has just shown me I didn’t truly understand it at all.
Take this hot cup of coffee and this cold jug of milk, the Brazilian physicist said as we sat in a café in Copenhagen. Bring them into contact and, sure enough, heat will flow from the hot object to the cold one, just as the German scientist Rudolf Clausius first stated formally in 1850. However, in some cases, de Oliveira explained, physicists have learned that the laws of quantum mechanics can drive heat flow the opposite way: from cold to hot.
This doesn’t really mean that the second law fails, he added as his coffee reassuringly cooled. It’s just that Clausius’ expression is the “classical limit” of a more complete formulation demanded by quantum physics.
Physicists began to appreciate the subtlety of this situation more than two decades ago and have been exploring the quantum mechanical version of the second law ever since. Now, de Oliveira, a postdoctoral researcher at the Technical University of Denmark, and colleagues have shown that the kind of “anomalous heat flow” that’s enabled at the quantum scale could have a convenient and ingenious use.
It can serve, they say, as an easy method for detecting “quantumness” — sensing, for instance, that an object is in a quantum “superposition” of multiple possible observable states, or that two such objects are entangled, with states that are interdependent — without destroying those delicate quantum phenomena. Such a diagnostic tool could be used to ensure that a quantum computer is truly using quantum resources to perform calculations. It might even help to sense quantum aspects of the force of gravity, one of the stretch goals of modern physics. All that’s needed, the researchers say, is to connect a quantum system to a second system that can store information about it, and to a heat sink: a body that’s able to absorb a lot of energy. With this setup, you can boost the transfer of heat to the heat sink, exceeding what would be permitted classically. Simply by measuring how hot the sink is, you could then detect the presence of superposition or entanglement in the quantum system.
Practical benefits aside, the research demonstrates a new aspect of a deep truth about thermodynamics: How heat and energy can be transformed and moved in physical systems is intimately bound up with information — what is or can be known about those systems. In this case, we “pay for” the anomalous heat flow by sacrificing stored information about the quantum system.
“I love the idea that thermodynamic quantities can signal quantum phenomena,” said the physicist Nicole Yunger Halpern of the University of Maryland. “The topic is fundamental and deep.”
Knowledge Is Power
The connection between the second law of thermodynamics and information was first explored in the 19th century by the Scottish physicist James Clerk Maxwell. To Maxwell’s distress, Clausius’ second law seemed to imply that pockets of heat will dissipate throughout the universe until all temperature differences disappear. In the process, the total entropy of the universe — crudely, a measure of how disordered and featureless it is — will inexorably increase. Maxwell realized that this trend would eventually remove all possibility of harnessing heat flows to do useful work, and the universe would settle into a sterile equilibrium pervaded by a uniform buzz of thermal motion: a “heat death.” That forecast would be troubling enough to anyone. It was anathema to the devoutly Christian Maxwell. But in a letter to his friend Peter Guthrie Tait in 1867, Maxwell claimed to have found a way to “pick a hole” in the second law.
He imagined a tiny being (later dubbed a demon) who could see the motions of individual molecules in a gas. The gas would fill a box that was divided in two by a wall with a trapdoor. By opening and closing the trapdoor selectively, the demon could sequester the faster-moving molecules in one compartment and the slower-moving ones in the other, making a hot gas and a cold one, respectively. By acting on the information it gathered about molecules’ motions, the demon thus reduced the entropy of the gas, creating a temperature gradient that could be used to do mechanical work, such as pushing a piston.
Scientists felt sure that Maxwell’s demon couldn’t really violate the second law, but it took nearly 100 years to figure out why not. The answer is that the information the demon collects and stores about the molecular motions will eventually fill up its finite memory. Its memory must then be erased and reset for it to keep working. The physicist Rolf Landauer showed in 1961 that this erasure burns energy and produces entropy — more entropy than is reduced by the demon’s sorting actions. Landauer’s analysis established an equivalence between information and entropy, implying that information itself can act as a thermodynamic resource: It can be transformed into work. Physicists experimentally demonstrated this information-to-energy conversion in 2010.
But quantum phenomena allow information to be processed in ways that classical physics does not permit — that’s the entire basis of technologies such as quantum computing and quantum cryptography. And that’s why quantum theory messes with the conventional second law.
Exploiting Correlations
Entangled quantum objects have mutual information: They are correlated, so we can discover properties of one by looking at the other. That in itself is not so strange; if you look at one of a pair of gloves and find it’s left-handed, you know the other is right-handed. But a pair of entangled quantum particles differs from gloves in a particular way: Whereas the handedness of gloves is already fixed before you look, this isn’t the case for the particles, according to quantum mechanics. Before we measure them, it’s undecided which value of the observable property each particle in the entangled pair has. At that stage the only things we can know are the probabilities of the possible combinations of values, such as 50% left-right and 50% right-left. Only when we measure the state of one of the particles do these possibilities resolve themselves into a definite outcome. In that measurement process, the entanglement is destroyed.
If gas molecules are entangled in this way, then a Maxwell’s demon can manipulate them more efficiently than if all the molecules are moving independently. If, say, the demon knows that any fast-moving molecule it sees coming is correlated in such a way that it will be trailed by another fast one just a moment later, the demon doesn’t have to bother observing the second particle before opening the trapdoor to admit it. The thermodynamic cost of (temporarily) foiling the second law is lowered.
In 2004, the quantum theorists Časlav Brukner of the University of Vienna and Vlatko Vedral, then at Imperial College London, pointed out that this means macroscopic thermodynamic measurements can be used as a “witness” to reveal the presence of quantum entanglement between particles. Under certain conditions, they showed, a system’s heat capacity or its response to an applied magnetic field should carry an imprint of entanglement, if it is present.
In a similar vein, other physicists calculated that you can extract more work from a warm body when there is quantum entanglement in the system than when it is purely classical.
And in 2008, the physicist Hossein Partovi of California State University identified a particularly dramatic implication of the way quantum entanglement can undermine preconceptions derived from classical thermodynamics. He realized that the presence of entanglement can actually reverse the spontaneous flow of heat from a hot object to a cold one, seemingly upending the second law itself.
That reversal is a special kind of refrigeration, Halpern said. And as usual with refrigeration, it doesn’t come for free (and so doesn’t truly subvert the second law). Classically, refrigerating an object takes work: We have to pump the heat the “wrong” way by consuming fuel, thereby repaying the entropy that’s lost by making the cold object colder and the hot object hotter. But in the quantum case, Halpern said, instead of burning fuel to achieve refrigeration, “you burn the correlations.” In other words, as the anomalous heat flow proceeds, the entanglement gets destroyed: Particles that initially had correlated properties become independent. “We can use the correlations as a resource to push heat in the opposite direction,” Halpern said.
In effect, the fuel here is information itself: specifically the mutual information of the entangled hot and cold bodies.
Two years later, David Jennings and Terry Rudolph of Imperial College London clarified what’s going on. They showed how the second law of thermodynamics can be reformulated to include the case where mutual information is present, and they calculated the limits on how much the classical heat flow can be altered and even reversed by the consumption of quantum correlations.
The Demon Knows
When quantum effects are in play, then, the second law isn’t so simple. But can we do anything useful with the way quantum physics loosens the bounds of thermodynamic laws? That’s one of the goals of the discipline called quantum thermodynamics, in which some researchers seek to make quantum engines that run more efficiently than classical ones, or quantum batteries that charge more quickly.
Patryk Lipka-Bartosik of the Center for Theoretical Physics at the Polish Academy of Sciences has sought practical applications in the other direction: using thermodynamics as a tool for probing quantum physics. Last year, he and his co-workers saw how to realize Brukner and Vedral’s 2004 idea to use thermodynamic properties as a witness of quantum entanglement. Their scheme involves hot and cold quantum systems that are correlated with each other, and a third system to mediate the heat flow between the two. We can think of this third system as a Maxwell’s demon, except now it has a “quantum memory” that can itself be entangled with the systems it is manipulating. Being entangled with the demon’s memory effectively links the hot and cold systems so that the demon can infer something about one from the properties of the other.
Such a quantum demon can act as a kind of catalyst, helping heat transfer happen by accessing correlations that are inaccessible otherwise. That is, because it is entangled with the hot and cold objects, the demon can divine and exploit all their correlations systematically. And, again like a catalyst, this third system returns to its original state once the heat exchange between the objects is completed. In this way, the process can boost the anomalous heat flow beyond what can be achieved without such a catalyst.
The paper this year by de Oliveira, co-authored by Lipka-Bartosik and Jonatan Bohr Brask of the Technical University of Denmark, uses some of these same ideas but with a crucial difference that turns the setup into a kind of thermometer for measuring quantumness. In the earlier work, the demonlike quantum memory interacted with a correlated pair of quantum systems, one hot and one cold. But in the latest work, it sits between a quantum system (say, an array of entangled quantum bits, or qubits, in a quantum computer) and a simple heat sink with which the quantum system is not directly entangled.
Because the memory is entangled with both the quantum system and the sink, it can again catalyze heat flow between them beyond what is possible classically. In that process, entanglement within the quantum system converts into extra heat that enters the sink. So measuring the energy stored in the heat sink (akin to reading its “temperature”) reveals the presence of entanglement in the quantum system. But since the system and sink aren’t themselves entangled, the measurement doesn’t affect the state of the quantum system. This gambit circumvents the notorious way that measurements destroy quantumness. “If you simply tried to make a measurement on the [quantum] system directly, you’d destroy its entanglement before the process could even unfold,” de Oliveira said.
The new scheme has the advantage of being simple and general, said Vedral, who is now at the University of Oxford. “These verification protocols are very important,” he said: Whenever some quantum computer company makes a new announcement about the performance of its latest device, he said the question always arises of how (or if) they really know that entanglement among the qubits is helping with the computation. A heat sink could serve as a detector of such quantum phenomena purely via its energy change. To implement the idea, you might designate one quantum bit as the memory whose state reveals that of other qubits, and then couple this memory qubit to a set of particles that will serve as the sink, whose energy you can measure. (One proviso, Vedral added, is that you need to have very good control over your system to be sure there aren’t other sources of heat flow contaminating the measurements. Another is that the method will not detect all entangled states.)
De Oliveira thinks that a system already exists for testing their idea experimentally. He and his colleagues are discussing that goal with Roberto Serra’s research group at the Federal University of ABC in São Paulo, Brazil. In 2016, Serra and colleagues used the magnetic orientations, or spins, of carbon and hydrogen atoms in molecules of chloroform as quantum bits between which they could transfer heat.
Using this setup, de Oliveira says it should be possible to exploit a quantum behavior — in this case coherence, meaning that the properties of two or more spins are evolving in phase with one another — to change the heat flow between the atoms. Coherence of qubits is essential for quantum computing, so being able to verify it by detecting anomalous heat exchange could be helpful.
The stakes could be even higher. Several research groups are trying to design experiments to determine whether gravity is a quantum force like the other three fundamental forces. Some of these efforts involve looking for quantum entanglement between two objects generated purely by their mutual gravitational attraction. Perhaps researchers could probe such gravity-induced entanglement by making simple thermodynamic measurements on them — thereby verifying (or not) that gravity really is quantized.
To study one of the deepest questions in physics, Vedral said, “wouldn’t it be lovely if you could do something as easy and macroscopic as this?”