Foundations of statistical mechanics from symmetries of entanglement
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:

^{[1]}
;
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
 Publication Date:
 Report Number(s):
 LAUR1521739
Journal ID: ISSN 13672630
 Grant/Contract Number:
 AC5206NA25396; 2015144057
 Type:
 Published Article
 Journal Name:
 New Journal of Physics
 Additional Journal Information:
 Journal Volume: 18; Journal Issue: 6; Journal ID: ISSN 13672630
 Publisher:
 IOP Publishing
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; statistical physics; entanglement; quantum symmetries
 OSTI Identifier:
 1256377
 Alternate Identifier(s):
 OSTI ID: 1256378; OSTI ID: 1329586
Deffner, Sebastian, and Zurek, Wojciech H. Foundations of statistical mechanics from symmetries of entanglement. United States: N. p.,
Web. doi:10.1088/13672630/18/6/063013.
Deffner, Sebastian, & Zurek, Wojciech H. Foundations of statistical mechanics from symmetries of entanglement. United States. doi:10.1088/13672630/18/6/063013.
Deffner, Sebastian, and Zurek, Wojciech H. 2016.
"Foundations of statistical mechanics from symmetries of entanglement". United States.
doi:10.1088/13672630/18/6/063013.
@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 = {10.1088/13672630/18/6/063013},
journal = {New Journal of Physics},
number = 6,
volume = 18,
place = {United States},
year = {2016},
month = {6}
}