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Entropy of Quantum States: Ambiguities · Around

2012

Entropy of Quantum States: Ambiguities

Balachandran, A. P., de Queiroz, A. R., Vaidya, S.

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The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states.

As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy.
This non-unique entropy can occur at zero temperature.
We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies.

Built on

A. P. Balachandran, G. Marmo, B. S. Skagerstam and A. Stern, Classical Topology and Quantum States
1991
Earlier work this paper cites.
R. Haag, Local Quantum Physics
1992
Earlier work this paper cites.
R. D. Sorkin, in Black Holes and Relativistic Stars
1998
Earlier work this paper cites.

Similar

N. Afshordi, S. Aslanbeigi and R. D. Sorkin, JHEP 1208
Original
2012
Cited alongside, same era.
N. Afshordi, M. Buck, F. Dowker, D. Rideout, R. D. Sorkin and Y. K. Yazdi, JHEP 1210
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Cited alongside, same era.
R. D. Sorkin, private communication
Cited in the paper.
B. Schroer, “A Course on: ’An Algebraic approach to nonperturbative quantum field theory’,” hep-th/9805093
Cited in the paper.
R. D. Sorkin, arXiv:1205.2953 [hep-th]
Original
Cited in the paper.
A. P. Balachandran, A. R. de Queiroz and S. Vaidya (in preparation)
Cited in the paper.
A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz and A. F. Reyes-Lega, arXiv:1205.2882 [quant-ph]
Original
Cited in the paper.

Then

A. P. Balachandran and A. R. de Queiroz, Phys. Rev. D 85
Original
2012
Closest in time.
D. Chruściński, Talk on “An Invitation to Open Quantum Systems” at Mathematical Structures in Quantum Systems and applications, Benasque 2012
2012
Closest in time.

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