Entanglement and the foundations of statistical mechanics

Nature Physics

Volumn 2, Issue 11, 2006, Pages 754-758

  Popescu, Sandu ^a,b   Short, Anthony J ^a   Winter, Andreas ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b HEWLETT PACKARD LABORATORIES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

STATISTICAL MECHANICS;

A-PRIORI PROBABILITIES; KEY ELEMENTS; TIME AVERAGES;

QUANTUM ENTANGLEMENT;

EID: 33750614339     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys444     Document Type: Article

References (22)

1. Mandl, F. Statistical Physics 2nd edn, Ch. 2, 40-41 (Wiley, New York, 1988).
2. Khinchin, A. I. Mathematical Foundations of Statistical Mechanics Ch. 3, 44-47 (Dover, New York, 1949).
3. Bocchieri, P. & Loinger, A. Ergodic foundation of quantum statistical mechanics. Phys. Rev. 114, 948-951 (1959).
4. Lloyd, S. Black Holes, Demons, and the Loss of Coherence. Ch. 3, 79-93, Thesis, Rockefeller Univ. (1988).
5. Gemmer, J., Michel, M. & Mahler, G. Quantum Thermodynamics Vol. 657 (Lecture Notes in Physics, Springer, Berlin, 2004).
6. Goldstein, S., Lebowitz, J. L., Tumulka, R. & Zanghì, N. Canonical typicality. Phys. Rev. Lett. 96, 050403 (2006).
7. Landau, L. D. & Lifshitz, E. M. Statistical Physics Ch. 3, 78-80 (Pergamon, London, 1958).
8. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information Ch. 9, 403-409 (Cambridge Univ. Press, Cambridge, 2000).
9. Lubkin, E. Entropy of an n-system from its correlation with a k-reservoir. J. Math. Phys. 19, 1028-1031 (1978).
10. Lloyd, S. & Pagels, H. Complexity as thermodynamic depth. Ann. Phys. 188, 186-213 (1988).
11. Page, D. N. Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291-1294 (1993).
12. Sen, S. Average entropy of a quantum subsystem. Phys. Rev. Lett. 77, 1-3 (1996).
13. Sommers, H.-J. & Zyczkowski, K. Statistical properties of random density matrices. J. Phys. A: Math. Gen. 37, 8457-8466 (2004).
14. Milman, V. D. & Schechtman, G. Asymptotic Theory of Finite-Dimensional Normed Spaces Ch. 2, 5-6 (Lecture Notes in Mathematics, Vol. 1,200, Springer, Berlin, 1986) and 140-141 Appendix V.
15. Hayden, P., Leung, D.W. & Winter, A. Aspects of generic entanglement. Commun. Math. Phys. 265, 95-117 (2006).
16. Lloyd, S. Capacity of the noisy quantum channel. Phys. Rev. A 55, 1613-1622 (1997).
17. Horodecki, M., Oppenheim, J. & Winter, A. Partial quantum information. Nature 436, 673-676 (2005).
18. Popescu, S., Short, A. J. & Winter, A. Entanglement and the foundations of statistical mechanics: Individual states vs averages. Preprint at 〈http://arxiv.org/abs/quant-ph/0511225〉 (2005).
19. Tasaki, H. From quantum dynamics to the canonical distribution: General picture and a rigorous example. Phys. Rev. Lett. 80, 1373-1376 (1998).
20. Michel, M., Mahler, G. & Gemmer, J. Fourier's law from Schrödinger dynamics. Phys. Rev. Lett. 95, 180602 (2005).
21. Breuer, H. P., Gemmer, J. & Michel, M. Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging. Phys. Rev. E 73, 016139 (2006).
22. Gemmer, J. & Michel, M. Thermalization of quantum systems by finite baths. Europhys. Lett. 73, 1-7 (2006).