Two papers investigate the thermodynamics of quantum systems

July 8, 2013 by Lisa Zyga, feature

(Left) A quantum system S is subjected to a (time-dependent) "protocol" that changes its energy. This results in some work made on S. (Right) The general quantum circuit scheme proposed by Oxford and Belfast to gather the quantum statistics of the work done on the system. A is an “auxiliary” quantum system that interacts with S through the joint operation G. The letter H stands for operations performed on A alone, which is then subjected to appropriate measurements. Credit: Mauro Paternostro
( —As one of the pillars of the natural sciences, thermodynamics plays an important role in all processes that involve heat, energy, and work. While the principles of thermodynamics can predict the amount of work done in classical systems, for quantum systems there is instead a distribution of many possible values of work. Two new papers published in Physical Review Letters have proposed theoretical schemes that would significantly ease the measurement of the statistics of work done by quantum systems.

The papers, "Extracting Quantum Work Statistics and Fluctuation Theorems by Single-Qubit Interferometry" led by Vlatko Vedral, a physics professor at the University of Oxford in the UK and the National University of Singapore; and "Measuring the Characteristic Function of the Work Distribution" led by the Quantum Technology Group at Queen's University in Belfast, UK, both investigate the thermodynamics of quantum systems.

Traditionally, the principles of thermodynamics have applied only to because of the inherent differences that arise at the .

"Take a classical system, and subject it to a transformation, which might result in some work done on/by the system," Mauro Paternostro, an associate professor (reader) and co-author of the work signed by the Belfast team, explained to "Now, consider a quantum mechanical system subjected to an analogous quantum evolution. As is inherently probabilistic, you do not have a definite, well defined value of work. On the contrary, you end up with a of possible values of work done on/by the system. Each value is associated with a possible 'trajectory' followed by the quantum system in its evolution due to the transformation. The expectation value of such a distribution is something close to the classical value of work performed on/by the analogous classical system. But the fact that it's a distribution (a quantum one!) makes it inherently different from classical mechanics.

As Paternostro explained, the quantum work distribution is very important because it's a key quantity in the framework of non-equilibrium quantum statistical mechanics, which is a formalism that describes the statistical and thermodynamical properties of a quantum system brought out of equilibrium. In addition, quantum analogies of classical fluctuation relations can be formulated in terms of the work distribution.

"So far, accessing the work distribution has found only limited success," Paternostro said. "Experimentally, [our proposal] would be a significant result, as the experimental determination of the work distribution would allow the assessment of quantum fluctuation relations, and thus the establishment of an experimental ground for quantum thermodynamics. Although some proposals have been put forward in the past, these were either too difficult, technically, or valid only in special cases.

"Our two proposals (the one by the Oxford group led by Prof. Vedral and the one from my group) managed to bypass such hindrances to (a) assess general processes, not just special cases, and (b) offer the promise for experimental implementability, as they are based on something known as phase-estimation strategies, which have found successful demonstrations in the past."

The scheme proposed by the Belfast team involves an ancilla-based measurement that can be applied to a micro- or nano-mechanical oscillator. On the other hand, Vedral and his coauthors' proposal uses Ramsey interferometry of a single probe within a trapped ion experiment. Both methods have the same goal: to measure the work distribution of quantum systems.

Understanding the work distribution of quantum systems could lead to a more comprehensive understanding of quantum thermodynamics, which in turn could lead to some interesting applications.

"A means of measuring the work distribution opens up the possibility of exploring, for the first time, a whole host of thermodynamic phenomena in quantum systems," said Ross Dorner, a PhD student of Professor Vedral and lead author of that paper. "The great thing about our scheme and that of the Belfast team is that they can be adapted to work in a whole range of current experimental technologies, including optical cavities, trapped neutral atoms and potentially many-body systems like Bose-Einstein condensates."

Paternostro added several other potential implications.

"Fundamentally, we could start exploring quantum thermodynamics, which puts together a genuine quantum approach and the rock-solid foundations of thermodynamics," he said. "We (and a few other researchers) are trying to do it from an information theoretic viewpoint, hoping to get new insight into this fascinating area. Practically, the grounding of quantum thermodynamics would imply the incorporation of quantum advantages in thermodynamical processes, such as the engineering of cycles, refrigerators and thermal machines. An example has been provided recently by myself and two colleagues, Dr. Adolfo del Campo (Los Alamos National Lab, US) and Dr. John Goold (University of Oxford and University College Cork, Republic of Ireland), by proposing the scheme for a friction-free quantum Otto machine. In a visionary way, we could build up a thermodynamical machine entirely based on quantum and offering better performances than their classical versions."

Both groups are currently working on experimental implementations of their proposals, which they hope will provide the first clear-cut reconstruction of the work distribution as the basic building block for quantum thermodynamics.

"Our group is working to implement these ideas in the laboratory," Dorner said. "We're also working on theoretical extensions to the idea which might help further improve the accuracy of the measurement scheme and also has applications to the thermometry of many-body ."

Explore further: Quantum engines must break down

More information: R. Dorner, et al. "Extracting QuantumWork Statistics and Fluctuation Theorems by Single-Qubit Interferometry." PRL 110, 230601 (2013). DOI: 10.1103/PhysRevLett.110.230601

L. Mazzola, et al. "Measuring the Characteristic Function of the Work Distribution." PRL 110, 230602 (2013). DOI: 10.1103/PhysRevLett.110.230602

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3.7 / 5 (3) Jul 08, 2013
Can it be inferred from this that the narrower the work distribution in a quantum system is (i.e. the smaller the standard deviation of the distribution) the more it behaves like a classical system?

Could one derive from this a measure of 'classicality' which might be useful in comparing quantum systems (especially in the view of their use as quantum computers)?
1 / 5 (1) Jul 08, 2013

What I got out of this is that given the very fast cycle rate that would be characteristic of quantum machines, the mean of the work distribution would be rather close to the experimentally observed distribution.

But as you indicated, a curve with large standard deviations would be less classical in this regard.
1 / 5 (6) Jul 08, 2013
it behaves like a classical system?

On the contrary: Their expectations seem to imply that as the statistics are different the potential efficiencies are different. Just as superconductivity and Bose Einstein Condensates (i.e. Quantum processes) obey different statistics and give results far exceeding classical possibilities.
1 / 5 (9) Jul 08, 2013
IMO the magnetic motors are assisted with quantum fluctuations, thus violating laws of classical thermodynamics. The magnetic domains are largest quantum objects which we can met in common life and they can be subject of negentropic effects, like the magnetic viscosity (magnetic undercooling) during the monopole/Dirac fermion state of magnetic domains. The spontaneous reversal of this state can be utilized for generation of usable mechanical work or for attenuation of electromagnetic field.
Doc Brown
Jul 08, 2013
This comment has been removed by a moderator.
1 / 5 (7) Jul 08, 2013
Mr. Valeria,

May I remind you again that you are violating the laws of classical patent protection. So please reverse your own state and desist from commenting on my proprietary work. You should attenuate your use of my work while trying to impress anyone who might be reading these comments. Plagiarism is an unseemly behavior in science minded people. Please stop.

Emmett Brown, Scientist
Hill Valley, U.S.A

Hey Doc, don't fret about it too much, no one posting here understands anything about ENTROPY anyway. All the above are happy with perpetual motion machines operating in a Universe where ENTROPY is a side issue that is simply a distraction to their train of thought. It would be a wasted hoot to even bother with one star ratings for all the perpetual motion that goes on here.
1 / 5 (10) Jul 08, 2013
Understanding the work distribution of quantum systems could lead to a more comprehensive understanding of quantum thermodynamics, which in turn could lead to some interesting applications.
"A means of measuring the work distribution opens up the possibility of exploring, for the first time, a whole host of thermodynamic phenomena in quantum systems," said Ross Dorner, a PhD student of Professor Vedral and lead author of that paper. …

Maybe or maybe not, because we do not know how the quantum mechanics works; understand the working mechanism of quantum mechanics as below could help the research.
1 / 5 (7) Jul 09, 2013
Doc Brown vs ValeriaT...whoops AWT in-fight? Benni, you know how to hurt a poor wait until I can un-break an egg Ha!

Ant-Phy, Fleet, Val, Q-st, & a few others have beat you to it as they sit inside the walls of their retirement homes & have figured out ways of "un-ringing" bells with their flat leaky infinite universes chock full of warp drives & wormholes & zero ENTROPY.

You'd think they'd go back to the star charts where they started their retirement careers at Physorg & are not challenged by their lack of scientific credentials, but instead they insist they want to lecture those of us whose careers are what they wished theirs had been. Benni- Electrical/Nuclear Engineer
5 / 5 (4) Jul 09, 2013
Benni- Electrical/Nuclear Engineer

Bzzt...electrical engineer and holder of a PhD - as well as scientist for more than 10 years. (and still at least 25 years from retirement)

You lose.

If you want to go into a credentials pissing contest make sure you're not standing close to the electric fence.
2.1 / 5 (7) Jul 09, 2013
Doc Brown vs ValeriaT...whoops AWT in-fight? Benni, you know how to hurt a poor wait until I can un-break an egg Ha!

Ant-Phy, Fleet, Val, Q-st, & a few others have beat you to it as they sit inside the walls of their retirement homes & have figured out ways of "un-ringing" bells with their flat leaky infinite universes chock full of warp drives & wormholes & zero ENTROPY.

Benni, child ya. I don't fit into that list except on one issue. Observationally, all evidence shows the universe to be flat within 0.01 %. That's pretty flat. Do ya have any observational evidence that is contrary to that. (Ya must answer no because there isn't any.)

Benni- Electrical/Nuclear Engineer

If much of the science ya post here is wrong, how would ya expect anyone to take that seriously. Maybe ya could find some way to insert E = mc^2 into conversation to prove that ya are an Electrical/Nuclear Engineer? Or "all energy is photonic", that was a good one too.
2.1 / 5 (7) Jul 11, 2013
I've noticed that people who brag about their job title or field(but always remain vague!) are extremely likely to be greenhorns who have crap positions and dream of future prospects that are likely out of their reach. Or simply liars.

You see, when you have actually accomplished many things in your life, you get a sense of self-confidence which precludes that type of behavior or the reinforcement that it seeks.
1.7 / 5 (6) Jul 11, 2013
I'm only 34. I had the best and most supportive(within their means) parents you could ever hope for and I got off to a good start on my career in my early 20s, though, and I am speaking entirely from my own experiences.
1.7 / 5 (6) Jul 11, 2013
Well, the simple fact is that I have always been highly exceptional among my peers at anything I click with. I was also an arrogant bastard. Picture McKay from Atlantis, except this particular one was one of the original 13 subjects used as a baseline for the Asperger's Syndrome test.

By the time I was 18, I had already completed a degree, won national pianist and organist competitions, was world-competitive in many FPS and RTS games, blah blah blah. By the time I was 25, I had earned over $1M selling currency in MMOs(using 18 PCs and a client/server botting system I wrote), etc. I ended up having a website that grew fast, and expanding that into a network that saw 50M uniques, and that is when the "career" I am referring to started. I now do extreme-scale hosting and consulting.

It's only been in the last 10 years that I really began to realize how little all of that matters when put into context given my downsides, and I really started seeing things differently since then.
1.7 / 5 (6) Jul 11, 2013

It very rarely matters if I think I'm all great and everything, even if I'm right. What matters is what matters.

It's not the exact same thing I was describing with the greenhorns, but it is similar in that you can get wrapped up in a self-image so much that it is detrimental to your behavior.

I wasn't really speaking on behalf of myself, though. After a few businesses, a few more acquisitions, and having to deal with people who think they are smart all the time(the people I consult and host), I've dealt with many of the types I described.
not rated yet Jul 12, 2013
it makes your 'credentials' look cheap.

That was the point. Credentials don't mean diddly squat in science. If your idea si good and your work is solid then it doesn't matter that you haven't finished high school.
If your work is shoddy and your conclusions are wrong then it doesn't matter whether your name is Einstein or you have worked 50 years inthe field.

Science is funny that way. Credentials accrue around good work as a byproduct - but they never help the science you currently do in any way.
Unlike in any other line of work you will NEVER find scientists judging the current work of their peers by their past work (or their credentials). The work has to stand on its own. Always.

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