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Canonical Typicality
Open accessAbstract
It is well known that a system weakly coupled to a heat bath is described by the canonical ensemble when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.
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Cited by
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Quantum mechanical evolution towards thermal equilibrium
Linden, N., Popescu, S., Short, A. J., & Winter, A. (2009) · Physical Review E · doi:10.1103/physreve.79.061103 · Cited by 625
Local Random Quantum Circuits are Approximate Polynomial-Designs
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Metadata
- Authors
- Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghì, N.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-02-08
- Volume
- 96
- Issue
- 5
- Pages
- 050403-050403
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3037704082
- Cited by
- 709
- References
- 0
- FWCI
- 10.09
- Type
- journal article
- Language
- en
- Open access
- green
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- Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghì, N. (2006). Canonical Typicality. Physical Review Letters. https://doi.org/10.1103/physrevlett.96.050403
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