Foundations of statistical mechanics from symmetries of entanglement

Deffner, Sebastian; Zurek, Wojciech H.

doi:10.1088/1367-2630/18/6/063013

Title: Foundations of statistical mechanics from symmetries of entanglement

Abstract

Envariance—entanglement assisted invariance—is a recently discovered symmetry of composite quantum systems. Here, we show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical equilibrium of a system $${ \mathcal S }$$ with Hamiltonian $${H}_{{ \mathcal S }}$$ is a fully energetically degenerate quantum state envariant under every unitary transformation. A representation of the canonical equilibrium then follows from simply counting degenerate energy states. Finally, our conceptually novel approach is free of mathematically ambiguous notions such as ensemble, randomness, etc., and, while it does not even rely on probability, it helps to understand its role in the quantum world.

Authors:

; Zurek, Wojciech H.

Publication Date:: Wed Jun 01 00:00:00 EDT 2016

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1256377

Alternate Identifier(s):: OSTI ID: 1256378; OSTI ID: 1329586

Report Number(s):: LA-UR-15-21739
Journal ID: ISSN 1367-2630

Grant/Contract Number:: AC52-06NA25396; 2015-144057

Resource Type:: Published Article

Journal Name:: New Journal of Physics

Additional Journal Information:: Journal Name: New Journal of Physics Journal Volume: 18 Journal Issue: 6; Journal ID: ISSN 1367-2630

Publisher:: IOP Publishing

Country of Publication:: United Kingdom

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; statistical physics; entanglement; quantum symmetries

Citation Formats


                    Deffner, Sebastian, and Zurek, Wojciech H. Foundations of statistical mechanics from symmetries of entanglement.  United Kingdom: N. p., 2016. 
Web.  doi:10.1088/1367-2630/18/6/063013.

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                    Deffner, Sebastian, & Zurek, Wojciech H. Foundations of statistical mechanics from symmetries of entanglement.  United Kingdom.  https://doi.org/10.1088/1367-2630/18/6/063013

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                    Deffner, Sebastian, and Zurek, Wojciech H. Wed .  
"Foundations of statistical mechanics from symmetries of entanglement".  United Kingdom.  https://doi.org/10.1088/1367-2630/18/6/063013.

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@article{osti_1256377,

  title        = {Foundations of statistical mechanics from symmetries of entanglement},

  author       = {Deffner, Sebastian and Zurek, Wojciech H.},

  abstractNote = {Envariance—entanglement assisted invariance—is a recently discovered symmetry of composite quantum systems. Here, we show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical equilibrium of a system ${ \mathcal S }$ with Hamiltonian ${H}_{{ \mathcal S }}$ is a fully energetically degenerate quantum state envariant under every unitary transformation. A representation of the canonical equilibrium then follows from simply counting degenerate energy states. Finally, our conceptually novel approach is free of mathematically ambiguous notions such as ensemble, randomness, etc., and, while it does not even rely on probability, it helps to understand its role in the quantum world.},

  doi          = {10.1088/1367-2630/18/6/063013},

  journal      = {New Journal of Physics},

  number       = 6,

  volume       = 18,

  place        = {United Kingdom},

  year         = {Wed Jun 01 00:00:00 EDT 2016},

  month        = {Wed Jun 01 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referenced in this record:

II. Illustrations of the dynamical theory of gases
journal, July 1860

Maxwell, J. C.
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 20, Issue 130
DOI: 10.1080/14786446008642902

Decoherence, einselection, and the quantum origins of the classical
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Zurek, Wojciech Hubert
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Probabilities from entanglement, Born’s rule $p_{k} = {∣ ψ_{k} ∣}^{2}$ from envariance
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Zurek, Wojciech Hubert
Physical Review A, Vol. 71, Issue 5
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Quantum Darwinism
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Zurek, Wojciech Hubert
Nature Physics, Vol. 5, Issue 3
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Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule
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Harris, Jérémie; Bouchard, Frédéric; Santamato, Enrico
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Uffink, Jos
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Entanglement and the foundations of statistical mechanics
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Popescu, Sandu; Short, Anthony J.; Winter, Andreas
Nature Physics, Vol. 2, Issue 11
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Canonical Typicality
journal, February 2006

Goldstein, Sheldon; Lebowitz, Joel L.; Tumulka, Roderich
Physical Review Letters, Vol. 96, Issue 5
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On LICQ and the uniqueness of Lagrange multipliers
journal, January 2013

Wachsmuth, Gerd
Operations Research Letters, Vol. 41, Issue 1
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From spooky foundations
journal, April 2015

Deffner, Sebastian
Nature Physics, Vol. 11, Issue 5
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Conditional expectation in an operator algebra, I
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Umegaki, Hisaharu
Tohoku Mathematical Journal, Vol. 6, Issue 2-3
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Works referencing / citing this record:

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism
journal, May 2018

Zurek, Wojciech Hubert
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2123
DOI: 10.1098/rsta.2018.0107

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism
journal, May 2018

Zurek, Wojciech Hubert
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2123
DOI: 10.1098/rsta.2018.0107

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Similar Records

Title: Foundations of statistical mechanics from symmetries of entanglement

Abstract

Citation Formats

II. Illustrations of the dynamical theory of gases journal, July 1860

Decoherence, einselection, and the quantum origins of the classical journal, May 2003

Probabilities from entanglement, Born’s rule p k = ∣ ψ k ∣ 2 from envariance journal, May 2005

Quantum Darwinism journal, March 2009

Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule journal, May 2016

Compendium of the foundations of classical statistical physics book, January 2007

Entanglement and the foundations of statistical mechanics journal, October 2006

Canonical Typicality journal, February 2006

On LICQ and the uniqueness of Lagrange multipliers journal, January 2013

From spooky foundations journal, April 2015

Conditional expectation in an operator algebra, I journal, January 1954

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism journal, May 2018

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism journal, May 2018

II. Illustrations of the dynamical theory of gases
journal, July 1860

Decoherence, einselection, and the quantum origins of the classical
journal, May 2003

Probabilities from entanglement, Born’s rule $p_{k} = {∣ ψ_{k} ∣}^{2}$ from envariance
journal, May 2005

Quantum Darwinism
journal, March 2009

Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule
journal, May 2016

Compendium of the foundations of classical statistical physics
book, January 2007

Entanglement and the foundations of statistical mechanics
journal, October 2006

Canonical Typicality
journal, February 2006

On LICQ and the uniqueness of Lagrange multipliers
journal, January 2013

From spooky foundations
journal, April 2015

Conditional expectation in an operator algebra, I
journal, January 1954

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism
journal, May 2018

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism
journal, May 2018