Christopher Jarzynski

University of Maryland

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Friday Oct 23, 2020 / 14:00-15:00 CEST

Work extraction from quantum coherences and their classical analogues

The role of quantum coherence as a potential thermodynamic resource, allowing for enhanced work extraction, has been investigated in detail in recent years. Less attention has been paid to the classical analogue of this problem, in which off-diagonal elements of the quantum density matrix, in the energy basis, are replaced by non-microcanonical statistical mixtures in phase space. I will compare the thermodynamic advantages offered by quantum coherences and those offered by classical non-microcanonical statistics, and will argue that the two cases lead to the same gains in work extraction. In this sense, while coherence may legitimately be viewed as a thermodynamic resource, it is not a uniquely quantal one.

Bio

College of Computer, Mathematical and Natural Sciences Headshots 11.28.2018

Chris Jarzynski received his bachelor’s degree from Princeton University (1987) and his PhD from the University of California, Berkeley (1994), both in Physics. After a postdoctoral fellowship at the Institute for Nuclear Theory in Seattle, he spent ten years in the Theoretical Division at Los Alamos National Laboratory. Since 2006 he has been a faculty member at the University of Maryland, College Park. His research interests include theoretical and computational work at the interface of physics, chemistry and biology, with a particular focus on nonequilibrium phenomena and the application of thermodynamic principles to microscopic systems.

Recorded video

2 replies

Mark Mitchison says:
October 23, 2020 at 4:30 pm

Thank you for a beautifully thought-provoking talk! I have been thinking about how to recover your inhomogeneous classical phase-space distributions from the semi-classical limit of a quantum state. It seems to me that such classical distributions only arise from underlying quantum states that have coherence in the energy eigenbasis (*). This leaves me wondering if the “classical coherence” that you discuss is really equivalent to quantum coherence.

Consider for example a harmonic oscillator, whose classical phase space is the x-p plane. Constant-energy shells are circles in this plane, p^2 + x^2 = constant, in appropriate units. Therefore classical distributions that are inhomogeneous within the energy shell are those that break rotational invariance, as you nicely illustrated on your slides. If I now think about a quantum harmonic oscillator, any state that is diagonal in the energy eigenbasis has a Wigner function that is rotationally symmetric in the x-p plane (I suspect this is also true of any other quasi-probability distribution). So a semi-classical phase-space distribution that is inhomogeneous in an energy shell can only arise from a state that has quantum coherence.

If I consider a more generic scenario such as a chaotic quantum many-body system, I come to a similar conclusion by appealing to the eigenstate thermalisation hypothesis. This tells me that each energy eigenstate is observationally indistinguishable from a microcanonical distribution at the same energy. Any statistical mixture of energy eigenstates is therefore indistinguishable from a mixture of microcanonical distributions, whose semi-classical approximation is clearly homogeneous within each energy shell. So I can only construct something that looks semi-classically inhomogeneous by taking a quantum superposition of energy eigenstates.

So to my question: is it possible that your “classical coherence” is really quantum coherence in disguise? Or am I missing something?

(*) To clarify, I start from the assumption that quantum mechanics is fundamentally correct, so that “classical systems” are really quantum-mechanical ones. That is, they can be described by a quantum state obeying quantum equations of motion, and the classical description is some appropriately coarse-grained version of the quantum one.
Janet Anders says:
October 23, 2020 at 3:37 pm

Dear Chris,
Thank you for a very nice and clear talk.
Ever since your nice paper with Quan and Rahav https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.031038 on the quantum-classical correspondence for work distributions (which appeared a few months after we had finished our work-from-coherence paper https://arxiv.org/abs/1502.02673) I have wondered if there exists a similar quantum-classical correspondence, for the coherence work.

In your talk today you described how you’ve found it – very nice and indeed enlightening in understanding the quantum to classical transition when it comes to coherences. Looking forward to reading the paper!

—
Today, questions were asked on what happens when correlations between the system S itself and external ancillas A are allowed.

In the published coherence work paper https://www.nature.com/articles/srep22174
we did discuss this within the quantum formalism, and found that MORE work can then be extracted than if operating on the system alone, and the difference, \delta, is a positive term quantifying the quantum correlations between S and A. It is related to but broader than quantum discord. See also supplement of the article, https://static-content.springer.com/esm/art%3A10.1038%2Fsrep22174/MediaObjects/41598_2016_BFsrep22174_MOESM1_ESM.pdf

Indeed it would be very interesting to know if the classical method you developed can assess how the role of correlations between quantum systems translates to the classical picture, and whether the same or a different gain in extractable work will result?