Quantum work and the thermodynamic cost of quantum measurements
Abstract
Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Lastly, a comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Ciudad Univ. Pabellon, Buenos Aires (Argentina)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1338795
- Alternate Identifier(s):
- OSTI ID: 1260862
- Report Number(s):
- LA-UR-16-21506
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1701795
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 1; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; atomic and nuclear physics
Citation Formats
Deffner, Sebastian, Paz, Juan Pablo, and Zurek, Wojciech H. Quantum work and the thermodynamic cost of quantum measurements. United States: N. p., 2016.
Web. doi:10.1103/PhysRevE.94.010103.
Deffner, Sebastian, Paz, Juan Pablo, & Zurek, Wojciech H. Quantum work and the thermodynamic cost of quantum measurements. United States. doi:10.1103/PhysRevE.94.010103.
Deffner, Sebastian, Paz, Juan Pablo, and Zurek, Wojciech H. Thu .
"Quantum work and the thermodynamic cost of quantum measurements". United States. doi:10.1103/PhysRevE.94.010103. https://www.osti.gov/servlets/purl/1338795.
@article{osti_1338795,
title = {Quantum work and the thermodynamic cost of quantum measurements},
author = {Deffner, Sebastian and Paz, Juan Pablo and Zurek, Wojciech H.},
abstractNote = {Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Lastly, a comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.},
doi = {10.1103/PhysRevE.94.010103},
journal = {Physical Review E},
number = 1,
volume = 94,
place = {United States},
year = {2016},
month = {7}
}
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Works referenced in this record:
Nonequilibrium work and entropy production by quantum projective measurements
journal, September 2013
- Yi, Juyeon; Kim, Yong Woon
- Physical Review E, Vol. 88, Issue 3
Thermodynamic length for far-from-equilibrium quantum systems
journal, February 2013
- Deffner, Sebastian; Lutz, Eric
- Physical Review E, Vol. 87, Issue 2
Fluctuation theorems for quantum processes
journal, September 2013
- Albash, Tameem; Lidar, Daniel A.; Marvian, Milad
- Physical Review E, Vol. 88, Issue 3
Conditional expectation in an operator algebra, I
journal, January 1954
- Umegaki, Hisaharu
- Tohoku Mathematical Journal, Vol. 6, Issue 2-3
Nonequilibrium potential and fluctuation theorems for quantum maps
journal, September 2015
- Manzano, Gonzalo; Horowitz, Jordan M.; Parrondo, Juan M. R.
- Physical Review E, Vol. 92, Issue 3
Fluctuation theorems for quantum master equations
journal, April 2006
- Esposito, Massimiliano; Mukamel, Shaul
- Physical Review E, Vol. 73, Issue 4
Experimental test of the quantum Jarzynski equality with a trapped-ion system
journal, December 2014
- An, Shuoming; Zhang, Jing-Ning; Um, Mark
- Nature Physics, Vol. 11, Issue 2
Thermodynamics of information
journal, February 2015
- Parrondo, Juan M. R.; Horowitz, Jordan M.; Sagawa, Takahiro
- Nature Physics, Vol. 11, Issue 2
Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems
journal, June 2005
- Allahverdyan, A. E.; Nieuwenhuizen, Th. M.
- Physical Review E, Vol. 71, Issue 6
Quantum work statistics of linear and nonlinear parametric oscillators
journal, October 2010
- Deffner, Sebastian; Abah, Obinna; Lutz, Eric
- Chemical Physics, Vol. 375, Issue 2-3
Generalized Clausius Inequality for Nonequilibrium Quantum Processes
journal, October 2010
- Deffner, Sebastian; Lutz, Eric
- Physical Review Letters, Vol. 105, Issue 17
Non-hermitian quantum thermodynamics
journal, March 2016
- Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh
- Scientific Reports, Vol. 6, Issue 1
Quantum fluctuation relations for ensembles of wave functions
journal, November 2013
- Campisi, Michele
- New Journal of Physics, Vol. 15, Issue 11
Decoherence, einselection, and the quantum origins of the classical
journal, May 2003
- Zurek, Wojciech Hubert
- Reviews of Modern Physics, Vol. 75, Issue 3
Colloquium : Quantum fluctuation relations: Foundations and applications
journal, July 2011
- Campisi, Michele; Hänggi, Peter; Talkner, Peter
- Reviews of Modern Physics, Vol. 83, Issue 3
Work Measurement as a Generalized Quantum Measurement
journal, December 2014
- Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo
- Physical Review Letters, Vol. 113, Issue 25
Information Processing and the Second Law of Thermodynamics: An Inclusive, Hamiltonian Approach
journal, October 2013
- Deffner, Sebastian; Jarzynski, Christopher
- Physical Review X, Vol. 3, Issue 4
Miscellanea in Elementary Quantum Mechanics, II
journal, April 1953
- Husimi, K.
- Progress of Theoretical Physics, Vol. 9, Issue 4
Quantum work statistics of charged Dirac particles in time-dependent fields
journal, September 2015
- Deffner, Sebastian; Saxena, Avadh
- Physical Review E, Vol. 92, Issue 3
Dissipation and lag in irreversible processes
journal, September 2009
- Vaikuntanathan, S.; Jarzynski, C.
- EPL (Europhysics Letters), Vol. 87, Issue 6
Nanoscale Heat Engine Beyond the Carnot Limit
journal, January 2014
- Roßnagel, J.; Abah, O.; Schmidt-Kaler, F.
- Physical Review Letters, Vol. 112, Issue 3
An information–theoretic equality implying the Jarzynski relation
journal, June 2012
- Vedral, Vlatko
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 27
Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements
journal, August 2014
- Fusco, L.; Pigeon, S.; Apollaro, T. J. G.
- Physical Review X, Vol. 4, Issue 3
Quantum Limit of Decoherence: Environment Induced Superselection of Energy Eigenstates
journal, June 1999
- Paz, Juan Pablo; Zurek, Wojciech Hubert
- Physical Review Letters, Vol. 82, Issue 26
Jarzynski Equality in -Symmetric Quantum Mechanics
journal, April 2015
- Deffner, Sebastian; Saxena, Avadh
- Physical Review Letters, Vol. 114, Issue 15
Quantum entropy production in phase space
journal, August 2013
- Deffner, Sebastian
- EPL (Europhysics Letters), Vol. 103, Issue 3
Single-Ion Heat Engine at Maximum Power
journal, November 2012
- Abah, O.; Roßnagel, J.; Jacob, G.
- Physical Review Letters, Vol. 109, Issue 20
Quantum Optomechanical Heat Engine
journal, April 2014
- Zhang, Keye; Bariani, Francesco; Meystre, Pierre
- Physical Review Letters, Vol. 112, Issue 15
Holevo's bound from a general quantum fluctuation theorem
journal, October 2012
- Kafri, Dvir; Deffner, Sebastian
- Physical Review A, Vol. 86, Issue 4
Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System
journal, October 2014
- Batalhão, Tiago B.; Souza, Alexandre M.; Mazzola, Laura
- Physical Review Letters, Vol. 113, Issue 14
Aspects of quantum work
journal, February 2016
- Talkner, Peter; Hänggi, Peter
- Physical Review E, Vol. 93, Issue 2
Nonequilibrium work distribution of a quantum harmonic oscillator
journal, February 2008
- Deffner, Sebastian; Lutz, Eric
- Physical Review E, Vol. 77, Issue 2
On Information and Sufficiency
journal, March 1951
- Kullback, S.; Leibler, R. A.
- The Annals of Mathematical Statistics, Vol. 22, Issue 1
Quantum-Classical Correspondence Principle for Work Distributions
journal, September 2015
- Jarzynski, Christopher; Quan, H. T.; Rahav, Saar
- Physical Review X, Vol. 5, Issue 3
Thermodynamics of Prediction
journal, September 2012
- Still, Susanne; Sivak, David A.; Bell, Anthony J.
- Physical Review Letters, Vol. 109, Issue 12
Fluctuation theorems: Work is not an observable
journal, May 2007
- Talkner, Peter; Lutz, Eric; Hänggi, Peter
- Physical Review E, Vol. 75, Issue 5
Foundations of statistical mechanics from symmetries of entanglement
journal, June 2016
- Deffner, Sebastian; Zurek, Wojciech H.
- New Journal of Physics, Vol. 18, Issue 6
Non-equilibrium equalities with unital quantum channels
journal, June 2013
- Rastegin, Alexey E.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 06
Jarzynski equality for quantum stochastic maps
journal, January 2014
- Rastegin, Alexey E.; Życzkowski, Karol
- Physical Review E, Vol. 89, Issue 1
All-Optical Nanomechanical Heat Engine
journal, May 2015
- Dechant, Andreas; Kiesel, Nikolai; Lutz, Eric
- Physical Review Letters, Vol. 114, Issue 18