bibkey: solfanellibuffonicuccolicampisi2019metrotropy
authors: Andrea Solfanelli; Lorenzo Buffoni; Alessandro Cuccoli; Michele Campisi
year: 2019
title: "Maximal energy extraction via quantum measurement"
doi: 10.1088/1742-5468/ab3721
url: https://arxiv.org/abs/1905.10262v2
claim: "The metrotropy, the maximal energy extractable from a finite quantum system by a nonselective rank-one projective measurement, satisfies M ≤ W/2 for stationary states, where W is the ergotropy, and M ≤ W in general. Whether M ≤ W/2 holds for non-stationary states is stated as open."
strata_touched:
  - D5/S3/Quantum/Thermal/MetrotropyHalfErgotropyRefutation
license: citation-only
triage: anchor

Solfanelli, Buffoni, Cuccoli and Campisi, Maximal energy extraction via quantum measurement

A. Solfanelli, L. Buffoni, A. Cuccoli and M. Campisi, J. Stat. Mech. (2019) 094003; arXiv:1905.10262v2. Quotations are from the v2 TeX source, with the source’s macro \Tr kept as written.

The ergotropy $\mathcal{W}$ is “the maximal amount of energy that can be extracted by means of unitary operations”, the minimum of the final energy $E^{\prime }={\sum }_k{E}_k⟨k|U\rho U^{†}|k⟩$ over unitaries subtracted from $E=\mathrm{Tr}H\rho$. The metrotropy $\mathcal{M}$ is “the maximal amount of energy that can be extracted from a finite quantum system by means of projective measurements”: a measurement maps

$${\rho }^{\prime }=\sum _k{\pi }_k\rho {\pi }_k$$

with a complete set of orthogonal projectors, assumed of rank one, ${\pi }_k=|{\psi }_k⟩⟨{\psi }_k|$, and $\mathcal{M}=E-\min E^{\prime }$. For stationary states the paper proves $\mathcal{M}\le \mathcal{W}/2$, with equality when the ergotropy permutation is an involution, and for non-stationary states it shows $\mathcal{M}\le \mathcal{W}$. Section 3.1 ends:

Whether the relation $\mathcal{M}\le \mathcal{W}/2$ holds in the case $[H,\rho ]\ne 0$ remains an open question.

Verified locator

Source: https://arxiv.org/abs/1905.10262v2

• DOI: https://doi.org/10.1088/1742-5468/ab3721 (Journal of Statistical Mechanics: Theory and Experiment 2019(9), article 094003; title, authors, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/1905.10262v2. The e-print member Metrotropy02.tex has 463 lines and md5 b4f183679366c63deb7a0ae5399f2fc9. Locations:
  • the abstract, l. 102; ergotropy, l. 130–157;
  • rank-one projective measurements, l. 164–175; the metrotropy formula, l. 272;
  • the remarks and the open question, l. 277–308.