Temperature and voltage measurement in quantum systems far from equilibrium
Abstract
In this work, we show that a local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a positive temperature solution exists whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a unique negative temperature. Voltage and temperature measurements are treated on an equal footing: They are simultaneously measured in a noninvasive manner, via a weakly coupled thermoelectric probe, defined by requiring vanishing charge and heat dissipation into the probe. Our results strongly suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice versa, is a misleading characterization of the state of a nonequilibrium quantum electron system. These results provide a firm mathematical foundation for voltage and temperature measurements far from equilibrium.
- Authors:
-
- Univ. of Arizona, Tucson, AZ (United States)
- Publication Date:
- Research Org.:
- Univ. of Arizona, Tucson, AZ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1535779
- Alternate Identifier(s):
- OSTI ID: 1329348
- Grant/Contract Number:
- SC0006699
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 15; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; nonequilibrium & irreversible thermodynamics; open quantum systems; quantum thermodynamics; quantum transport
Citation Formats
Shastry, Abhay, and Stafford, Charles A. Temperature and voltage measurement in quantum systems far from equilibrium. United States: N. p., 2016.
Web. doi:10.1103/physrevb.94.155433.
Shastry, Abhay, & Stafford, Charles A. Temperature and voltage measurement in quantum systems far from equilibrium. United States. https://doi.org/10.1103/physrevb.94.155433
Shastry, Abhay, and Stafford, Charles A. Wed .
"Temperature and voltage measurement in quantum systems far from equilibrium". United States. https://doi.org/10.1103/physrevb.94.155433. https://www.osti.gov/servlets/purl/1535779.
@article{osti_1535779,
title = {Temperature and voltage measurement in quantum systems far from equilibrium},
author = {Shastry, Abhay and Stafford, Charles A.},
abstractNote = {In this work, we show that a local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a positive temperature solution exists whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a unique negative temperature. Voltage and temperature measurements are treated on an equal footing: They are simultaneously measured in a noninvasive manner, via a weakly coupled thermoelectric probe, defined by requiring vanishing charge and heat dissipation into the probe. Our results strongly suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice versa, is a misleading characterization of the state of a nonequilibrium quantum electron system. These results provide a firm mathematical foundation for voltage and temperature measurements far from equilibrium.},
doi = {10.1103/physrevb.94.155433},
journal = {Physical Review B},
number = 15,
volume = 94,
place = {United States},
year = {Wed Oct 19 00:00:00 EDT 2016},
month = {Wed Oct 19 00:00:00 EDT 2016}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 15 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Quantitative Measurement with Scanning Thermal Microscope by Preventing the Distortion Due to the Heat Transfer through the Air
journal, October 2011
- Kim, Kyeongtae; Chung, Jaehun; Hwang, Gwangseok
- ACS Nano, Vol. 5, Issue 11
Scanning thermal profiler
journal, December 1986
- Williams, C. C.; Wickramasinghe, H. K.
- Applied Physics Letters, Vol. 49, Issue 23
Quantum Theory of an Optical Maser. I. General Theory
journal, July 1967
- Scully, Marlan O.; Lamb, Willis E.
- Physical Review, Vol. 159, Issue 2
Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs
journal, May 2007
- Roy, Dibyendu; Dhar, Abhishek
- Physical Review B, Vol. 75, Issue 19
Quantitative Thermometry of Nanoscale Hot Spots
journal, January 2012
- Menges, Fabian; Riel, Heike; Stemmer, Andreas
- Nano Letters, Vol. 12, Issue 2, p. 596-601
Onset of Energy Dissipation in Ballistic Atomic Wires
journal, May 2002
- Agraït, Nicolás; Untiedt, Carlos; Rubio-Bollinger, Gabino
- Physical Review Letters, Vol. 88, Issue 21
Local and effective temperatures of quantum driven systems
journal, January 2010
- Caso, Alvaro; Arrachea, Liliana; Lozano, Gustavo S.
- Physical Review B, Vol. 81, Issue 4
Semiclassical theory of shot noise in mesoscopic conductors
journal, August 1996
- de Jong, M. J. M.; Beenakker, C. W. J.
- Physica A: Statistical Mechanics and its Applications, Vol. 230, Issue 1-2
High-resolution spatial mapping of the temperature distribution of a Joule self-heated graphene nanoribbon
journal, October 2011
- Yu, Young-Jun; Han, Melinda Y.; Berciaud, Stéphane
- Applied Physics Letters, Vol. 99, Issue 18
Tunneling through a controllable vacuum gap
journal, January 1982
- Binnig, G.; Rohrer, H.; Gerber, Ch.
- Applied Physics Letters, Vol. 40, Issue 2
Energy Gap Induced by Friedel Oscillations Manifested as Transport Asymmetry at Monolayer-Bilayer Graphene Boundaries
journal, February 2014
- Clark, Kendal W.; Zhang, X. -G.; Gu, Gong
- Physical Review X, Vol. 4, Issue 1
Optical Methods of Atomic Orientation and of Magnetic Resonance*
journal, January 1957
- Kastler, Alfred
- Journal of the Optical Society of America, Vol. 47, Issue 6
Small normal-metal loop coupled to an electron reservoir
journal, August 1985
- Büttiker, M.
- Physical Review B, Vol. 32, Issue 3
Four-terminal resistance of a ballistic quantum wire
journal, May 2001
- de Picciotto, R.; Stormer, H. L.; Pfeiffer, L. N.
- Nature, Vol. 411, Issue 6833
Tunable quantum temperature oscillations in graphene nanostructures
journal, March 2015
- Bergfield, Justin P.; Ratner, Mark A.; Stafford, Charles A.
- Physical Review B, Vol. 91, Issue 12
Cold spots in quantum systems far from equilibrium: Local entropies and temperatures near absolute zero
journal, December 2015
- Shastry, Abhay; Stafford, Charles A.
- Physical Review B, Vol. 92, Issue 24
Local Transport Measurements at Mesoscopic Length Scales Using Scanning Tunneling Potentiometry
journal, June 2013
- Wang, Weigang; Munakata, Ko; Rozler, Michael
- Physical Review Letters, Vol. 110, Issue 23
Spatial extent of a Landauer residual-resistivity dipole in graphene quantified by scanning tunnelling potentiometry
journal, March 2015
- Willke, Philip; Druga, Thomas; Ulbrich, Rainer G.
- Nature Communications, Vol. 6, Issue 1
Experimental measurement of scattering coefficients in mesoscopic conductors
journal, October 1992
- Shepard, K. L.; Roukes, M. L.; van der Gaag, B. P.
- Physical Review B, Vol. 46, Issue 15
Vibrational and electronic heating in nanoscale junctions
journal, December 2010
- Ward, Daniel R.; Corley, David A.; Tour, James M.
- Nature Nanotechnology, Vol. 6, Issue 1
Reciprocal Relations in Irreversible Processes. I.
journal, February 1931
- Onsager, Lars
- Physical Review, Vol. 37, Issue 4
The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport
journal, December 2013
- Bedkihal, Salil; Bandyopadhyay, Malay; Segal, Dvira
- The European Physical Journal B, Vol. 86, Issue 12
Spectral mapping of thermal conductivity through nanoscale ballistic transport
journal, June 2015
- Hu, Yongjie; Zeng, Lingping; Minnich, Austin J.
- Nature Nanotechnology, Vol. 10, Issue 8
Ballistic thermal rectification in asymmetric three-terminal mesoscopic dielectric systems
journal, October 2010
- Ming, Yi; Wang, Zhe Xian; Ding, Ze Jun
- New Journal of Physics, Vol. 12, Issue 10
Temperature in non-equilibrium states: a review of open problems and current proposals
journal, October 2003
- Casas-Vázquez, J.; Jou, D.
- Reports on Progress in Physics, Vol. 66, Issue 11
Quantum heat transfer in harmonic chains with self-consistent reservoirs: Exact numerical simulations
journal, July 2011
- Bandyopadhyay, Malay; Segal, Dvira
- Physical Review E, Vol. 84, Issue 1
ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
journal, February 2009
- Jacquet, Philippe A.
- Journal of Statistical Physics, Vol. 134, Issue 4
Local temperature of out-of-equilibrium quantum electron systems
journal, July 2014
- Meair, J.; Bergfield, J. P.; Stafford, C. A.
- Physical Review B, Vol. 90, Issue 3
Four-Point Resistance of Individual Single-Wall Carbon Nanotubes
journal, October 2005
- Gao, B.; Chen, Y. F.; Fuhrer, M. S.
- Physical Review Letters, Vol. 95, Issue 19
Thermopower with broken time-reversal symmetry
journal, November 2011
- Saito, Keiji; Benenti, Giuliano; Casati, Giulio
- Physical Review B, Vol. 84, Issue 20
Local temperature of an interacting quantum system far from equilibrium
journal, June 2016
- Stafford, Charles A.
- Physical Review B, Vol. 93, Issue 24
Scanning tunneling microscopy
journal, March 1983
- Binnig, G.; Rohrer, H.
- Surface Science, Vol. 126, Issue 1-3
Local potentiometry using a multiprobe scanning tunneling microscope
journal, August 2008
- Bannani, A.; Bobisch, C. A.; Möller, R.
- Review of Scientific Instruments, Vol. 79, Issue 8
Thermoelectric transport of mesoscopic conductors coupled to voltage and thermal probes
journal, November 2011
- Sánchez, David; Serra, Llorenç
- Physical Review B, Vol. 84, Issue 20
Many-body theory of electronic transport in single-molecule heterojunctions
journal, June 2009
- Bergfield, J. P.; Stafford, C. A.
- Physical Review B, Vol. 79, Issue 24
Definition and measurement of the electrical and thermal resistances
journal, July 1981
- Engquist, H. - L.; Anderson, P. W.
- Physical Review B, Vol. 24, Issue 2
Voltage and dephasing probes in mesoscopic conductors: A study of full-counting statistics
journal, January 2007
- Förster, Heidi; Samuelsson, Peter; Pilgram, Sebastian
- Physical Review B, Vol. 75, Issue 3
Asymmetry in the Magnetoconductance of Metal Wires and Loops
journal, October 1986
- Benoit, A. D.; Washburn, S.; Umbach, C. P.
- Physical Review Letters, Vol. 57, Issue 14
Nonequilibrium Many-Body Theory of Quantum Systems
book, March 2013
- Stefanucci, Gianluca; van Leeuwen, Robert
Scanning tunneling potentiometry
journal, February 1986
- Muralt, P.; Pohl, D. W.
- Applied Physics Letters, Vol. 48, Issue 8
Thermoelectric corrections to quantum voltage measurement
journal, December 2014
- Bergfield, Justin P.; Stafford, Charles A.
- Physical Review B, Vol. 90, Issue 23
Local temperatures and heat flow in quantum driven systems
journal, April 2011
- Caso, Alvaro; Arrachea, Liliana; Lozano, Gustavo S.
- Physical Review B, Vol. 83, Issue 16
Role of quantum coherence in series resistors
journal, March 1986
- Büttiker, M.
- Physical Review B, Vol. 33, Issue 5
Interfacial Charge States in Graphene on SiC Studied by Noncontact Scanning Nonlinear Dielectric Potentiometry
journal, June 2015
- Yamasue, Kohei; Fukidome, Hirokazu; Funakubo, Kazutoshi
- Physical Review Letters, Vol. 114, Issue 22
Scanning Probe Microscopy
book, January 2007
- Kalinin, Sergei; Gruverman, Alexei
- Springer New York, NY
Heat conduction in molecular transport junctions
journal, April 2007
- Galperin, Michael; Nitzan, Abraham; Ratner, Mark A.
- Physical Review B, Vol. 75, Issue 15
Ultra-High Vacuum Scanning Thermal Microscopy for Nanometer Resolution Quantitative Thermometry
journal, May 2012
- Kim, Kyeongtae; Jeong, Wonho; Lee, Woochul
- ACS Nano, Vol. 6, Issue 5, p. 4248-4257
Thermoelectric Signatures of Coherent Transport in Single-Molecule Heterojunctions
journal, August 2009
- Bergfield, J. P.; Stafford, C. A.
- Nano Letters, Vol. 9, Issue 8
Chemical potential oscillations near a barrier in the presence of transport
journal, August 1989
- Büttiker, M.
- Physical Review B, Vol. 40, Issue 5
Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie
journal, January 1854
- Clausius, R.
- Annalen der Physik und Chemie, Vol. 169, Issue 12
Infrared and Optical Masers
journal, December 1958
- Schawlow, A. L.; Townes, C. H.
- Physical Review, Vol. 112, Issue 6
Heat dissipation in atomic-scale junctions
journal, June 2013
- Lee, Woochul; Kim, Kyeongtae; Jeong, Wonho
- Nature, Vol. 498, Issue 7453
Thermoelectric Effects in Nanoscale Junctions
journal, January 2009
- Dubi, Yonatan; Di Ventra, Massimiliano
- Nano Letters, Vol. 9, Issue 1
Conductance of a disordered linear chain including inelastic scattering events
journal, April 1990
- D’Amato, Jorge L.; Pastawski, Horacio M.
- Physical Review B, Vol. 41, Issue 11
Quantum-statistical current correlations in multilead chaotic cavities
journal, July 1997
- van Langen, S. A.; Büttiker, M.
- Physical Review B, Vol. 56, Issue 4
Probing Maxwell’s Demon with a Nanoscale Thermometer
journal, May 2013
- Bergfield, Justin P.; Story, Shauna M.; Stafford, Robert C.
- ACS Nano, Vol. 7, Issue 5
Fourier’s law: Insight from a simple derivation
journal, April 2009
- Dubi, Y.; Di Ventra, M.
- Physical Review E, Vol. 79, Issue 4
Anisotropy in Conductance of a Quasi-One-Dimensional Metallic Surface State Measured by a Square Micro-Four-Point Probe Method
journal, July 2003
- Kanagawa, Taizo; Hobara, Rei; Matsuda, Iwao
- Physical Review Letters, Vol. 91, Issue 3
Radiative heat transfer in the extreme near field
journal, December 2015
- Kim, Kyeongtae; Song, Bai; Fernández-Hurtado, Víctor
- Nature, Vol. 528, Issue 7582
Atomic Force Microscope
journal, March 1986
- Binnig, G.; Quate, C. F.; Gerber, Ch.
- Physical Review Letters, Vol. 56, Issue 9
Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge
journal, January 1986
- Sivan, U.; Imry, Y.
- Physical Review B, Vol. 33, Issue 1
Voltage distribution and phase-breaking scattering in the quantum Hall regime
journal, July 1996
- Ando, Tsuneya
- Surface Science, Vol. 361-362
Efficiency of three-terminal thermoelectric transport under broken time-reversal symmetry
journal, April 2013
- Balachandran, Vinitha; Benenti, Giuliano; Casati, Giulio
- Physical Review B, Vol. 87, Issue 16
Understanding Non-equilibrium Thermodynamics
book, January 2008
- Lebon, G.; Jou, D.; Casas-Vázquez, J.
Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach
journal, February 2015
- Esposito, Massimiliano; Ochoa, Maicol A.; Galperin, Michael
- Physical Review Letters, Vol. 114, Issue 8
Scanning Thermal Microscopy
journal, August 1999
- Majumdar, A.
- Annual Review of Materials Science, Vol. 29, Issue 1
Landauer formula for the current through an interacting electron region
journal, April 1992
- Meir, Yigal; Wingreen, Ned S.
- Physical Review Letters, Vol. 68, Issue 16
Coherent and sequential tunneling in series barriers
journal, January 1988
- Buttiker, M.
- IBM Journal of Research and Development, Vol. 32, Issue 1
Magnetic field symmetries of nonlinear transport with elastic and inelastic scattering
journal, October 2013
- Bedkihal, Salil; Bandyopadhyay, Malay; Segal, Dvira
- Physical Review B, Vol. 88, Issue 15
Strong Bounds on Onsager Coefficients and Efficiency for Three-Terminal Thermoelectric Transport in a Magnetic Field
journal, February 2013
- Brandner, Kay; Saito, Keiji; Seifert, Udo
- Physical Review Letters, Vol. 110, Issue 7
Temperature and voltage probes far from equilibrium
journal, March 2012
- Jacquet, Ph. A.; Pillet, C. -A.
- Physical Review B, Vol. 85, Issue 12
The effective temperature
journal, November 2011
- Cugliandolo, Leticia F.
- Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 48
Giant Thermoelectric Effect from Transmission Supernodes
journal, August 2010
- Bergfield, Justin P.; Solis, Michelle A.; Stafford, Charles A.
- ACS Nano, Vol. 4, Issue 9
Atomic Force Microscope. [原子間力顕微鏡]
journal, January 1991
- Tsuda, Nobuhiro
- Journal of the Japan Society for Precision Engineering, Vol. 57, Issue 7
Scanning tunneling microscopy
journal, April 1985
- Binnig, G.; Rohrer, H.
- Surface Science Letters, Vol. 152-153
Scanning Probe Microscopy
journal, January 2008
- Morita, Seizo
- Journal of the Vacuum Society of Japan, Vol. 51, Issue 12
Scanning tunneling microscopy
journal, January 2000
- Binnig, G.; Rohrer, H.
- IBM Journal of Research and Development, Vol. 44, Issue 1.2
ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
text, January 2008
- Jacquet, Philippe A.
- arXiv
Ballistic Thermal Rectification in Asymmetric Three-Terminal Mesoscopic Dielectric Systems
text, January 2009
- Ming, Yi; Wang, Zhe Xian; Ding, Ze Jun
- arXiv
Giant Thermoelectric Effect from Transmission Supernodes
text, January 2010
- Bergfield, J. P.; Solis, M.; Stafford, C. A.
- arXiv
Quantum heat transfer in harmonic chains with self consistent reservoirs: Exact numerical simulations
text, January 2011
- Bandyopadhyay, Malay; Segal, Dvira
- arXiv
Temperature and Voltage Probes Far from Equilibrium
text, January 2011
- Jacquet, Ph. A.; Pillet, C. -A.
- arXiv
Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field
text, January 2013
- Brandner, Kay; Saito, Keiji; Seifert, Udo
- arXiv
Cold spots in quantum systems far from equilibrium: local entropies and temperatures near absolute zero
text, January 2015
- Shastry, Abhay; Stafford, Charles A.
- arXiv
Four-point resistance of individual single-wall carbon nanotubes
text, January 2005
- Gao, B.; Chen, Y. F.; Fuhrer, M. S.
- arXiv
Heat conduction in molecular transport junctions
text, January 2006
- Galperin, Michael; Ratner, Mark A.; Nitzan, Abraham
- arXiv
Semiclassical theory of shot noise in mesoscopic conductors
text, January 1996
- de Jong, M. J. M.; Beenakker, C. W. J.
- arXiv
Works referencing / citing this record:
The third law of thermodynamics in open quantum systems
journal, August 2019
- Shastry, Abhay; Xu, Yiheng; Stafford, Charles A.
- The Journal of Chemical Physics, Vol. 151, Issue 6
Thermionic cooling devices based on resonant-tunneling AlGaAs/GaAs heterostructure
journal, January 2018
- Bescond, M.; Logoteta, D.; Michelini, F.
- Journal of Physics: Condensed Matter, Vol. 30, Issue 6
Quantum thermodynamics of nanoscale steady states far from equilibrium
journal, April 2018
- Taniguchi, Nobuhiko
- Physical Review B, Vol. 97, Issue 15
Quantum thermodynamics of nanoscale steady states far from equilibrium
text, January 2017
- Taniguchi, Nobuhiko
- arXiv