thermodynamics – Quantum Frontiers

Film noir and quantum thermo

Shayan Majidy — Thu, 23 May 2024 01:00:00 +0000

In four months, I’ll embark on the adventure of a lifetime—fatherhood. To prepare, I’ve been honing a quintessential father skill—storytelling. If my son inherits even a fraction of my tastes, he’ll soon develop a passion for film noir detective stories. … Continue reading →

Noncommuting charges are much like Batman

Shayan Majidy — Thu, 21 Mar 2024 01:00:00 +0000

Understanding a character’s origins enriches their narrative and motivates their actions. Take Batman as an example: without knowing his backstory, he appears merely as a billionaire who might achieve more by donating his wealth rather than masquerading as a bat … Continue reading →

Discoveries at the Dibner

Twesh Upadhyaya — Tue, 06 Feb 2024 13:17:41 +0000

This past summer, our quantum thermodynamics research group had the wonderful opportunity to visit the Dibner Rare Book Library in D.C. Located in a small corner of the Smithsonian National Museum of American History, tucked away behind flashier exhibits, the Dibner is home to thousands of rare books and manuscripts, some dating back many centuries.

Our advisor, Nicole Yunger Halpern, has a special connection to the Dibner, having interned there as an undergrad. She’s remained in contact with the head librarian, Lilla Vekerdy. For our visit, the two of them curated a large spread of scientific work related to thermodynamics, physics, and mathematics. The tomes ranged from a 1500s print of Euclid’s Elements to originals of Einstein’s manuscripts with hand-written notes in the margin.

The print of Euclid’s Elements was one of the standout exhibits. It featured a number of foldout nets of 3D solids, which had been cut and glued into the book by hand. Several hundred copies of this print are believed to have been made, each of them containing painstakingly crafted paper models. At the time, this technique was an innovation, resulting from printers’ explorations of the then-young art of large-scale book publication.

Another interesting exhibit was rough notes on ideal gases written by Planck, one of the fathers of quantum mechanics. Ideal gases are the prototypical model in statistical mechanics, capturing to high accuracy the behaviour of real gases within certain temperatures and pressures. The notes contained comparisons between Boltzmann, Ehrenfest, and Planck’s own calculations for classical and quantum ideal gases. Though the prose was in German, some results were instantly recognizable, such as the plot of the specific heat of a classical ideal gas, showing the stepwise jump as degrees of freedom freeze out.

Looking through these great physicists’ rough notes, scratched-out ideas, and personal correspondences was a unique experience, helping humanize them and place their work in historical context. Understanding the history of science doesn’t just need to be for historians, it can be useful for scientists themselves! Seeing how scientists persevered through unknowns, grappling with doubts and incomplete knowledge to generate new ideas, is inspiring. But when one only reads the final, polished result in a modern textbook, it can be difficult to appreciate this process of discovery. Another reason to study the historical development of scientific results is that core concepts have a way of arising time and again across science. Recognizing how these ideas have arisen in the past is insightful. Examining the creative processes of great scientists before us helps develop our own intuition and skillset.

Thanks to our advisor for this field trip – and make sure to check out the Dibner next time you’re in DC!

Can Thermodynamics Resolve the Measurement Problem?

Tom Rivlin — Sun, 10 Sep 2023 18:06:25 +0000

At the recent Quantum Thermodynamics conference in Vienna (coming next year to the University of Maryland!), during an expert panel Q&A session, one member of the audience asked “can quantum thermodynamics address foundational problems in quantum theory?”

That stuck with me, because that’s exactly what my research is about. So naturally, I’d say the answer is yes! In fact, here in the group of Marcus Huber at the Technical University of Vienna, we think thermodynamics may have something to say about the biggest quantum foundations problem of all: the measurement problem.

It’s sort of the iconic mystery of quantum mechanics: we know that an electron can be in two places at once – in a ‘superposition’ – but when we measure it, it’s only ever seen to be in one place, picked seemingly at random from the two possibilities. We say the state has ‘collapsed’.

What’s going on here? Thanks to Bell’s legendary theorem, we know that the answer can’t just be that it was always actually in one place and we just didn’t know which option it was – it really was in two places at once until it was measured¹. But also, we don’t see this effect for sufficiently large objects. So how can this ‘two-places-at-once’ thing happen at all, and why does it stop happening once an object gets big enough?

Here, we already see hints that thermodynamics is involved, because even classical thermodynamics says that big systems behave differently from small ones. And interestingly, thermodynamics also hints that the narrative so far can’t be right. Because when taken at face value, the ‘collapse’ model of measurement breaks all three laws of thermodynamics.

Imagine an electron in a superposition of two energy levels: a combination of being in its ground state and first excited state. If we measure it and it ‘collapses’ to being only in the ground state, then its energy has decreased: it went from having some average of the ground and excited energies to just having the ground energy. The first law of thermodynamics says (crudely) that energy is conserved, but the loss of energy is unaccounted for here.

Next, the second law says that entropy always increases. One form of entropy represents your lack of information about a system’s state. Before the measurement, the system was in one of two possible states, but afterwards it was in only one state. So speaking very broadly, our uncertainty about its state, and hence the entropy, is reduced. (The third law is problematic here, too.)

There’s a clear explanation here: while the system on its own decreases its entropy and doesn’t conserve energy, in order to measure something, we must couple the system to a measuring device. That device’s energy and entropy changes must account for the system’s changes.

This is the spirit of our measurement model². We explicitly include the detector as a quantum object in the record-keeping of energy and information flow. In fact, we also include the entire environment surrounding both system and device – all the lab’s stray air molecules, photons, etc. Then the idea is to describe a measurement process as propagating a record of a quantum system’s state into the surroundings without collapsing it.

A schematic representation of a system spreading information into an environment (from Schwarzhans et al., with permission)

But talking about quantum systems interacting with their environments is nothing new. The “decoherence” model from the 70s, which our work builds on, says quantum objects become less quantum when buffeted by a larger environment.

The problem, though, is that decoherence describes how information is lost into an environment, and so usually the environment’s dynamics aren’t explicitly calculated: this is called an open-system approach. By contrast, in the closed-system approach we use, you model the dynamics of the environment too, keeping track of all information. This is useful because conventional collapse dynamics seems to destroy information, but every other fundamental law of physics seems to say that information can’t be destroyed.

This all allows us to track how information flows from system to surroundings, using the “Quantum Darwinism” (QD) model of W.H. Żurek. Whereas decoherence describes how environments affect systems, QD describes how quantum systems impact their environments by spreading information into them. The QD model says that the most ‘classical’ information – the kind most consistent with classical notions of ‘being in one place’, etc. – is the sort most likely to ‘survive’ the decoherence process.

QD then further asserts that this is the information that’s most likely to be copied into the environment. If you look at some of a system’s surroundings, this is what you’d most likely see. (The ‘Darwinism’ name is because certain states are ‘selected for’ and ‘replicate’³.)

So we have a description of what we want the post-measurement state to look like: a decohered system, with its information redundantly copied into its surrounding environment. The last piece of the puzzle, then, is to ask how a measurement can create this state. Here, we finally get to the dynamics part of the thermodynamics, and introduce equilibration.

Earlier we said that even if the system’s entropy decreases, the detector’s entropy (or more broadly the environment’s) should go up to compensate. Well, equilibration maximizes entropy. In particular, equilibration describes how a system tends towards a particular ‘equilibrium’ state, because the system can always increase its entropy by getting closer to it.

It’s usually said that systems equilibrate if put in contact with an external environment (e.g. a can of beer cooling in a fridge), but we’re actually interested in a different type of equilibration called equilibration on average. There, we’re asking for the state that a system stays roughly close to, on average, over long enough times, with no outside contact. That means it never actually decoheres, it just looks like it does for certain observables. (This actually implies that nothing ever actually decoheres, since open systems are only an approximation you make when you don’t want to track all of the environment.)

Equilibration is the key to the model. In fact, we call our idea the Measurement-Equilibration Hypothesis (MEH): we’re asserting that measurement is an equilibration process. Which makes the final question: what does all this mean for the measurement problem?

In the MEH framework, when someone ‘measures’ a quantum system, they allow some measuring device, plus a chaotic surrounding environment, to interact with it. The quantum system then equilibrates ‘on average’ with the environment, and spreads information about its classical states into the surroundings. Since you are a macroscopically large human, any measurement you do will induce this sort of equilibration to happen, meaning you will only ever have access to the classical information in the environment, and never see superpositions. But no collapse is necessary, and no information is lost: rather some information is only much more difficult to access in all the environment noise, as happens all the time in the classical world.

It’s tempting to ask what ‘happens’ to the outcomes we don’t see, and how nature ‘decides’ which outcome to show to us. Those are great questions, but in our view, they’re best left to philosophers⁴. For the question we care about: why measurements look like a ‘collapse’, we’re just getting started with our Measurement-Equilibration Hypothesis – there’s still lots to do in our explorations of it. We think the answers we’ll uncover in doing so will form an exciting step forward in our understanding of the weird and wonderful quantum world.

Members of the MEH team at a kick-off meeting for the project in Vienna in February 2023. Left to right: Alessandro Candeloro, Marcus Huber, Emanuel Schwarzhans, Tom Rivlin, Sophie Engineer, Veronika Baumann, Nicolai Friis, Felix C. Binder, Mehul Malik, Maximilian P.E. Lock, Pharnam Bakhshinezhad

Acknowledgements: Big thanks to the rest of the MEH team for all the help and support, in particular Dr. Emanuel Schwarzhans and Dr. Lock for reading over this piece!)

Here are a few choice references (by no means meant to be comprehensive!)

Quantum Thermodynamics (QTD) Conference 2023: https://qtd2023.conf.tuwien.ac.at/
QTD 2024: https://qtd-hub.umd.edu/event/qtd-conference-2024/
Bell’s Theorem: https://plato.stanford.edu/entries/bell-theorem/
The first MEH paper: https://arxiv.org/abs/2302.11253
A review of decoherence: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.715
Quantum Darwinism: https://www.nature.com/articles/nphys1202
Measurements violate the 3^rd law: https://quantum-journal.org/papers/q-2020-01-13-222/
More on the 3^rd and QM: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.010332
Equilibration on average: https://iopscience.iop.org/article/10.1088/0034-4885/79/5/056001/meta
Objectivity: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.032122

There is a perfectly valid alternative with other weird implications: that it was always just in one place, but the world is intrinsically non-local. Most physicists prefer to save locality over realism, though. ︎
First proposed in this paper by Schwarzhans, Binder, Huber, and Lock: https://arxiv.org/abs/2302.11253 ︎
In my opinion… it’s a brilliant theory with a terrible name! Sure, there’s something akin to ‘selection pressure’ and ‘reproduction’, but there aren’t really any notions of mutation, adaptation, fitness, generations… Alas, the name has stuck. ︎
I actually love thinking about this question, and the interpretations of quantum mechanics more broadly, but it’s fairly orthogonal to the day-to-day research on this model. ︎

Identical twins and quantum entanglement

Shayan Majidy — Mon, 13 Mar 2023 00:00:00 +0000

“If I had a nickel for every unsolicited and very personal health question I’ve gotten at parties, I’d have paid off my medical school loans by now,” my doctor friend complained. As a physicist, I can somewhat relate. I occasionally find myself nodding along politely to people’s eccentric theories about the universe. A gentleman once explained to me how twin telepathy (the phenomenon where, for example, one twin feels the other’s pain despite being in separate countries) comes from twins’ brains being entangled in the womb. Entanglement is a nonclassical correlation that can exist between spatially separated systems. If two objects are entangled, it’s possible to know everything about both of them together but nothing about either one. Entangling two particles (let alone full brains) over tens of kilometres (let alone full countries) is incredibly challenging. “Using twins to study entanglement, that’ll be the day,” I thought. Well, my last paper did something like that.

In theory, a twin study consists of two people that are as identical as possible in every way except for one. What that allows you to do is isolate the effect of that one thing on something else. Aleksander Lasek (postdoc at QuICS), David Huse (professor of physics at Princeton), Nicole Yunger Halpern (NIST physicist and Quantum Frontiers blogger), and I were interested in isolating the effects of quantities’ noncommutation (explained below) on entanglement. To do so, we first built a pair of twins and then compared them.

Consider a well-insulated thermos filled with soup. The heat and the number of “soup particles” inside the thermos are conserved. So the energy and the number of “soup particles” are conserved quantities. In classical physics, conserved quantities commute. This means that we can simultaneously measure the amount of each conserved quantity in our system, like the energy and number of soup particles. However, in quantum mechanics, this needn’t be true. Measuring one property of a quantum system can change another measurement’s outcome.

Conserved quantities’ noncommutation in thermodynamics has led to some interesting results. For example, it’s been shown that conserved quantities’ noncommutation can decrease the rate of entropy production. For the purposes of this post, entropy production is something that limits engine efficiency—how well engines can convert fuel to useful work. For example, if your car engine had zero entropy production (which is impossible), it would convert 100% of the energy in your car’s fuel into work that moved your car along the road. Current car engines can convert about 30% of this energy, so it’s no wonder that people are excited about the prospective application of decreasing entropy production. Other results (like this one and that one) have connected noncommutation to potentially hindering thermalization—the phenomenon where systems interact until they have similar properties, like when a cup of coffee cools. Thermalization limits memory storage and battery lifetimes. Thus, learning how to resist thermalization could also potentially lead to better technologies, such as longer-lasting batteries.

One can measure the amount of entanglement within a system, and as quantum particles thermalize, they entangle. Given the above results about thermalization, we might expect that noncommutation would decrease entanglement. Testing this expectation is where the twins come in.

Say we built a pair of twins that were identical in every way except for one. Nancy, the noncommuting twin, has some features that don’t commute, say, her hair colour and height. This means that if we measure her height, we’ll have no idea what her hair colour is. For Connor, the commuting twin, his hair colour and height commute, so we can determine them both simultaneously. Which twin has more entanglement? It turns out it’s Nancy.

Disclaimer: This paragraph is written for an expert audience. Our actual models consist of 1D chains of pairs of qubits. Each model has three conserved quantities (“charges”), which are sums over local charges on the sites. In the noncommuting model, the three local charges are tensor products of Pauli matrices with the identity (XI, YI, ZI). In the commuting model, the three local charges are tensor products of the Pauli matrices with themselves (XX, YY, ZZ). The paper explains in what sense these models are similar. We compared these models numerically and analytically in different settings suggested by conventional and quantum thermodynamics. In every comparison, the noncommuting model had more entanglement on average.

Our result thus suggests that noncommutation increases entanglement. So does charges’ noncommutation promote or hinder thermalization? Frankly, I’m not sure. But I’d bet the answer won’t be in the next eccentric theory I hear at a party.

Building a Koi pond with Lie algebras

Shayan Majidy — Mon, 31 Jan 2022 02:00:00 +0000

When I was growing up, one of my favourite places was the shabby all-you-can-eat buffet near our house. We’d walk in, my mom would approach the hostess to explain that, despite my being abnormally large for my age, I qualified for kids-eat-free, and I would peel away to stare at the Koi pond. The display of different fish rolling over one another was bewitching. Ten-year-old me would have been giddy to build my own Koi pond, and now I finally have. However, I built one using Lie algebras.

The different fish swimming in the Koi pond are, in many ways, like charges being exchanged between subsystems. A “charge” is any globally conserved quantity. Examples of charges include energy, particles, electric charge, or angular momentum. Consider a system consisting of a cup of coffee in your office. The coffee will dynamically exchange charges with your office in the form of heat energy. Still, the total energy of the coffee and office is conserved (assuming your office walls are really well insulated). In this example, we had one type of charge (heat energy) and two subsystems (coffee and office). Consider now a closed system consisting of many subsystems and many different types of charges. The closed system is like the finite Koi pond with different charges like the different fish species. The charges can move around locally, but the total number of charges is globally fixed, like how the fish swim around but can’t escape the pond. Also, the presence of one type of charge can alter another’s movement, just as a big fish might block a little one’s path.

Unfortunately, the Koi pond analogy reaches its limit when we move to quantum charges. Classically, charges commute. This means that we can simultaneously determine the amount of each charge in our system at each given moment. In quantum mechanics, this isn’t necessarily true. In other words, classically, I can count the number of glossy fish and matt fish. But, in quantum mechanics, I can’t.

So why does this matter? Subsystems exchanging charges are prevalent in thermodynamics. Quantum thermodynamics extends thermodynamics to include small systems and quantum effects. Noncommutation underlies many important quantum phenomena. Hence, studying the exchange of noncommuting charges is pivotal in understanding quantum thermodynamics. Consequently, noncommuting charges have emerged as a rapidly growing subfield of quantum thermodynamics. Many interesting results have been discovered from no longer assuming that charges commute (such as these). Until recently, most of these discoveries have been theoretical. Bridging these discoveries to experimental reality requires Hamiltonians (functions that tell you how your system evolves in time) that move charges locally but conserve them globally. Last year it was unknown whether these Hamiltonians exist, what they look like generally, how to build them, and for what charges you could find them.

Nicole Yunger Halpern (NIST physicist, my co-advisor, and Quantum Frontiers blogger) and I developed a prescription for building Koi ponds for noncommuting charges. Our prescription allows you to systematically build Hamiltonians that overtly move noncommuting charges between subsystems while conserving the charges globally. These Hamiltonians are built using Lie algebras, abstract mathematical tools that can describe many physical quantities (including everything in the standard model of particle physics and space-time metric). Our results were recently published in npj QI. We hope that our prescription will bolster the efforts to bridge the results of noncommuting charges to experimental reality.

In the end, a little group theory was all I needed for my Koi pond. Maybe I’ll build a treehouse next with calculus or a remote control car with combinatorics.

What matters to me, and why?

Nicole Yunger Halpern — Mon, 27 Jun 2016 03:50:29 +0000

Students at my college asked every Tuesday. They gathered in a white, windowed room near the center of campus. “We serve,” read advertisements, “soup, bread, and food for thought.” One professor or visitor would discuss human rights, family, religion, or another pepper in the chili of life.

I joined occasionally. I listened by the window, in the circle of chairs that ringed the speaker. Then I ventured from college into physics.

The questions “What matters to you, and why?” have chased me through physics. I ask experimentalists and theorists, professors and students: Why do you do science? Which papers catch your eye? Why have you devoted to quantum information more years than many spouses devote to marriages?

One physicist answered with another question. Chris Jarzynski works as a professor at the University of Maryland. He studies statistical mechanics—how particles typically act and how often particles act atypically; how materials shine, how gases push back when we compress them, and more.

“How,” Chris asked, “should we quantify precision?”

Chris had in mind nonequilibrium fluctuation theorems. Out-of-equilibrium systems have large-scale properties, like temperature, that change significantly.¹ Examples include white-bean soup cooling at a “What matters” lunch. The soup’s temperature drops to room temperature as the system approaches equilibrium.

Nonequilibrium. Tasty, tasty nonequilibrium.

Some out-of-equilibrium systems obey fluctuation theorems. Fluctuation theorems are equations derived in statistical mechanics. Imagine a DNA molecule floating in a watery solution. Water molecules buffet the strand, which twitches. But the strand’s shape doesn’t change much. The DNA is in equilibrium.

You can grab the strand’s ends and stretch them apart. The strand will leave equilibrium as its length changes. Imagine pulling the strand to some predetermined length. You’ll have exerted energy.

How much? The amount will vary if you repeat the experiment. Why? This trial began with the DNA curled this way; that trial began with the DNA curled that way. During this trial, the water batters the molecule more; during that trial, less. These discrepancies block us from predicting how much energy you’ll exert. But suppose you pick a number W. We can form predictions about the probability that you’ll have to exert an amount W of energy.

How do we predict? Using nonequilibrium fluctuation theorems.

Fluctuation theorems matter to me, as Quantum Frontiers regulars know. Why? Because I’ve written enough fluctuation-theorem articles to test even a statistical mechanic’s patience. More seriously, why do fluctuation theorems matter to me?

Fluctuation theorems fill a gap in the theory of statistical mechanics. Fluctuation theorems relate nonequilibrium processes (like the cooling of soup) to equilibrium systems (like room-temperature soup). Physicists can model equilibrium. But we know little about nonequilibrium. Fluctuation theorems bridge from the known (equilibrium) to the unknown (nonequilibrium).

Experiments take place out of equilibrium. (Stretching a DNA molecule changes the molecule’s length.) So we can measure properties of nonequilibrium processes. We can’t directly measure properties of equilibrium processes, which we can’t perform experimentally. But we can measure an equilibrium property indirectly: We perform nonequilibrium experiments, then plug our data into fluctuation theorems.

Which equilibrium property can we infer about? A free-energy difference, denoted by ΔF. Every equilibrated system (every room-temperature soup) has a free energy F. F represents the energy that the system can exert, such as the energy available to stretch a DNA molecule. Imagine subtracting one system’s free energy, F₁, from another system’s free energy, F₂. The subtraction yields a free-energy difference, ΔF = F₂ – F₁. We can infer the value of a ΔF from experiments.

How should we evaluate those experiments? Which experiments can we trust, and which need repeating?

Those questions mattered little to me, before I met Chris Jarzynski. Bridging equilibrium with nonequilibrium mattered to me, and bridging theory with experiment. Not experimental nitty-gritty.

I deserved a dunking in white-bean soup.

Suppose you performed infinitely many trials—stretched a DNA molecule infinitely many times. In each trial, you measured the energy exerted. You processed your data, then substituted into a fluctuation theorem. You could infer the exact value of ΔF.

But we can’t perform infinitely many trials. Imprecision mars our inference about ΔF. How does the imprecision relate to the number of trials performed?²

Chris and I adopted an information-theoretic approach. We quantified precision with a parameter . Suppose you want to estimate ΔF with some precision. How many trials should you expect to need to perform? We bounded the number of trials, using an entropy. The bound tightens an earlier estimate of Chris’s. If you perform trials, you can estimate ΔF with a percent error that we estimated. We illustrated our results by modeling a gas.

I’d never appreciated the texture and richness of precision. But richness precision has: A few decimal places distinguish Albert Einstein’s general theory of relativity from Isaac Newton’s 17th-century mechanics. Particle physicists calculate constants of nature to many decimal places. Such a calculation earned a nod on physicist Julian Schwinger’s headstone. Precision serves as the bread and soup of much physics. I’d sniffed the importance of precision, but not tasted it, until questioned by Chris Jarzynski.

The questioning continues. My college has discontinued its “What matters” series. But I ask scientist after scientist—thoughtful human being after thoughtful human being—“What matters to you, and why?” Asking, listening, reading, calculating, and self-regulating sharpen my answers those questions. My answers often squish beneath the bread knife in my cutlery drawer of criticism. Thank goodness that repeating trials can reduce our errors.

¹Or large-scale properties that will change. Imagine connecting the ends of a charged battery with a wire. Charge will flow from terminal to terminal, producing a current. You can measure, every minute, how quickly charge is flowing: You can measure how much current is flowing. The current won’t change much, for a while. But the current will die off as the battery nears depletion. A large-scale property (the current) appears constant but will change. Such a capacity to change characterizes nonequilibrium steady states (NESSes). NESSes form our second example of nonequilibrium states. Many-body localization forms a third, quantum example.

²Readers might object that scientists have tools for quantifying imprecision. Why not apply those tools? Because ΔF equals a logarithm, which is nonlinear. Other authors’ proposals appear in references 1-13 of our paper. Charlie Bennett addressed a related problem with his “acceptance ratio.” (Bennett also blogged about evil on Quantum Frontiers last month.)

Discourse in Delft

Nicole Yunger Halpern — Mon, 30 Nov 2015 03:00:00 +0000

A camel strolled past, yards from our window in the Applied-Sciences Building.

I hadn’t expected to see camels at TU Delft, aka the Delft University of Technology, in Holland. I breathed, “Oh!” and turned to watch until the camel followed its turbaned leader out of sight. Nelly Ng, the PhD student with whom I was talking, followed my gaze and laughed.

Nelly works in Stephanie Wehner’s research group. Stephanie—a quantum cryptographer, information theorist, thermodynamicist, and former Caltech postdoc—was kind enough to host me for half August. I arrived at the same time as TU Delft’s first-year undergrads. My visit coincided with their orientation. The orientation involved coffee hours, team-building exercises, and clogging the cafeteria whenever the Wehner group wanted lunch.

And, as far as I could tell, a camel.

Not even a camel could unseat Nelly’s and my conversation. Nelly, postdoc Mischa Woods, and Stephanie are the Wehner-group members who study quantum and small-scale thermodynamics. I study quantum and small-scale thermodynamics, as Quantum Frontiers stalwarts might have tired of hearing. The four of us exchanged perspectives on our field.

Mischa knew more than Nelly and I about clocks; Nelly knew more about catalysis; and I knew more about fluctuation relations. We’d read different papers. We’d proved different theorems. We explained the same phenomena differently. Nelly and I—with Mischa and Stephanie, when they could join us—questioned and answered each other almost perpetually, those two weeks.

We talked in our offices, over lunch, in the group discussion room, and over tea at TU Delft’s Quantum Café. We emailed. We talked while walking. We talked while waiting for Stephanie to arrive so that she could talk with us.

The site of many a tête-à-tête.

The copiousness of the conversation drained me. I’m an introvert, formerly “the quiet kid” in elementary school. Early some mornings in Delft, I barricaded myself in the visitors’ office. Late some nights, I retreated to my hotel room or to a canal bank. I’d exhausted my supply of communication; I had no more words for anyone. Which troubled me, because I had to finish a paper. But I regret not one discussion, for three reasons.

First, we relished our chats. We laughed together, poked fun at ourselves, commiserated about calculations, and confided about what we didn’t understand.

We helped each other understand, second. As I listened to Mischa or as I revised notes about a meeting, a camel would stroll past a window in my understanding. I’d see what I hadn’t seen before. Mischa might be explaining which quantum states represent high-quality clocks. Nelly might be explaining how a quantum state ξ can enable a state ρ to transform into a state σ. I’d breathe, “Oh!” and watch the mental camel follow my interlocutor through my comprehension.

Nelly’s, Mischa’s, and Stephanie’s names appear in the acknowledgements of the paper I’d worried about finishing. The paper benefited from their explanations and feedback.

Third, I left Delft with more friends than I’d had upon arriving. Nelly, Mischa, and I grew to know each other, to trust each other, to enjoy each other’s company. At the end of my first week, Nelly invited Mischa and me to her apartment for dinner. She provided pasta; I brought apples; and Mischa brought a sweet granola-and-seed mixture. We tasted and enjoyed more than we would have separately.

Dinner with Nelly and Mischa.

I’ve written about how Facebook has enhanced my understanding of, and participation in, science. Research involves communication. Communication can challenge us, especially many of us drawn to science. Let’s shoulder past the barrier. Interlocutors point out camels—and hot-air balloons, and lemmas and theorems, and other sources of information and delight—that I wouldn’t spot alone.

With gratitude to Stephanie, Nelly, Mischa, the rest of the Wehner group (with whom I enjoyed talking), QuTech and TU Delft.

During my visit, Stephanie and Delft colleagues unveiled the “first loophole-free Bell test.” Their paper sent shockwaves (AKA camels) throughout the quantum community. Scott Aaronson explains the experiment here.

Toward physical realizations of thermodynamic resource theories

Nicole Yunger Halpern — Mon, 14 Sep 2015 02:05:00 +0000

“This is your arch-nemesis.”

The thank-you slide of my presentation remained onscreen, and the question-and-answer session had begun. I was presenting a seminar about thermodynamic resource theories (TRTs), models developed by quantum-information theorists for small-scale exchanges of heat and work. The audience consisted of condensed-matter physicists who studied graphene and photonic crystals. I was beginning to regret my topic’s abstractness.

The question-asker pointed at a listener.

“This is an experimentalist,” he continued, “your arch-nemesis. What implications does your theory have for his lab? Does it have any? Why should he care?”

I could have answered better. I apologized that quantum-information theorists, reared on the rarefied air of Dirac bras and kets, had developed TRTs. I recalled the baby steps with which science sometimes migrates from theory to experiment. I could have advocated for bounding, with idealizations, efficiencies achievable in labs. I should have invoked the connections being developed with fluctuation results, statistical mechanical theorems that have withstood experimental tests.

The crowd looked unconvinced, but I scored one point: The experimentalist was not my arch-nemesis.

“My new friend,” I corrected the questioner.

His question has burned in my mind for two years. Experiments have inspired, but not guided, TRTs. TRTs have yet to drive experiments. Can we strengthen the connection between TRTs and the natural world? If so, what tools must resource theorists develop to predict outcomes of experiments? If not, are resource theorists doing physics?

A Q&A more successful than mine.

I explore answers to these questions in a paper released today. Ian Durham and Dean Rickles were kind enough to request a contribution for a book of conference proceedings. The conference, “Information and Interaction: Eddington, Wheeler, and the Limits of Knowledge” took place at the University of Cambridge (including a graveyard thereof), thanks to FQXi (the Foundational Questions Institute).

What, I asked my advisor, does one write for conference proceedings?

“Proceedings are a great opportunity to get something off your chest,” John said.

That seminar Q&A had sat on my chest, like a pet cat who half-smothers you while you’re sleeping, for two years. Theorists often justify TRTs with experiments.^* Experimentalists, an argument goes, are probing limits of physics. Conventional statistical mechanics describe these regimes poorly. To understand these experiments, and to apply them to technologies, we must explore TRTs.

Does that argument not merit testing? If experimentalists observe the extremes predicted with TRTs, then the justifications for, and the timeliness of, TRT research will grow.

Something to get off your chest. Like the contents of a conference-proceedings paper, according to my advisor.

You’ve read the paper’s introduction, the first eight paragraphs of this blog post. (Who wouldn’t want to begin a paper with a mortifying anecdote?) Later in the paper, I introduce TRTs and their role in one-shot statistical mechanics, the analysis of work, heat, and entropies on small scales. I discuss whether TRTs can be realized and whether physicists should care. I identify eleven opportunities for shifting TRTs toward experiments. Three opportunities concern what merits realizing and how, in principle, we can realize it. Six adjustments to TRTs could improve TRTs’ realism. Two more-out-there opportunities, though less critical to realizations, could diversify the platforms with which we might realize TRTs.

One opportunity is the physical realization of thermal embezzlement. TRTs, like thermodynamic laws, dictate how systems can and cannot evolve. Suppose that a state cannot transform into a state : . An ancilla , called a catalyst, might facilitate the transformation: . Catalysts act like engines used to extract work from a pair of heat baths.

Engines degrade, so a realistic transformation might yield , wherein resembles . For certain definitions of “resembles,”** TRTs imply, one can extract arbitrary amounts of work by negligibly degrading . Detecting the degradation—the work extraction’s cost—is difficult. Extracting arbitrary amounts of work at a difficult-to-detect cost contradicts the spirit of thermodynamic law.

The spirit, not the letter. Embezzlement seems physically realizable, in principle. Detecting embezzlement could push experimentalists’ abilities to distinguish between close-together states and . I hope that that challenge, and the chance to violate the spirit of thermodynamic law, attracts researchers. Alternatively, theorists could redefine “resembles” so that doesn’t rub the law the wrong way.

The paper’s broadness evokes a caveat of Arthur Eddington’s. In 1927, Eddington presented Gifford Lectures entitled The Nature of the Physical World. Being a physicist, he admitted, “I have much to fear from the expert philosophical critic.” Specializing in TRTs, I have much to fear from the expert experimental critic. The paper is intended to point out, and to initiate responses to, the lack of physical realizations of TRTs. Some concerns are practical; some, philosophical. I expect and hope that the discussion will continue…preferably with more cooperation and charity than during that Q&A.

If you want to continue the discussion, drop me a line.

^*So do theorists-in-training. I have.

**A definition that involves the trace distance.

I spy with my little eye…something algebraic.

Nicole Yunger Halpern — Mon, 17 Nov 2014 17:02:52 +0000

Look at this picture.

Does any part of it surprise you? Look more closely.

Now? Try crossing your eyes.

Do you see a boy’s name?

I spell “Peter” with two e’s, but “Piotr” and “Pyotr” appear as authors’ names in papers’ headers. Finding “Petr” in a paper shouldn’t have startled me. But how often does “Gretchen” or “Amadeus” materialize in an equation?

When I was little, my reading list included Eye Spy, Where’s Waldo?, and Puzzle Castle. The books teach children to pay attention, notice details, and evaluate ambiguities.

That’s what physicists do. The first time I saw the picture above, I saw a variation on “Peter.” I was reading (when do I not?) about the intersection of quantum information and thermodynamics. The authors were discussing heat and algebra, not saints or boys who picked pecks of pickled peppers. So I looked more closely.

Each letter resolved into part of a story about a physical system. The P represents a projector. A projector is a mathematical object that narrows one’s focus to a particular space, as blinders on a horse do. The E tells us which space to focus on: a space associated with an amount E of energy, like a country associated with a GDP of $500 billion.

Some of the energy E belongs to a heat reservoir. We know so because “reservoir” begins with r, and R appears in the picture. A heat reservoir is a system, like a colossal bathtub, whose temperature remains constant. The Greek letter , pronounced “tau,” represents the reservoir’s state. The reservoir occupies an equilibrium state: The bath’s large-scale properties—its average energy, volume, etc.—remain constant. Never mind about jacuzzis.

Piecing together the letters, we interpret the picture as follows: Imagine a vast, constant-temperature bathtub (R). Suppose we shut the tap long enough ago that the water in the tub has calmed (). Suppose the tub neighbors a smaller system—say, a glass of Perrier.^* Imagine measuring how much energy the bath-and-Perrier composite contains (P). Our measurement device reports the number E.

Quite a story to pack into five letters. Didn’t Peter deserve a second glance?

The equation’s right-hand side forms another story. I haven’t seen Peters on that side, nor Poseidons nor Gallahads. But look closely, and you will find a story.

The images above appear in “Fundamental limitations for quantum and nanoscale thermodynamics,” published by Michał Horodecki and Jonathan Oppenheim in Nature Communications in 2013.

^*Experts: The ρ_S that appears in the first two images represents the smaller system. The tensor product represents the reservoir-and-smaller-system composite.