Thermal Pure Quantum States at Finite Temperature

H. Nakamura and M. Takahashi, J. Phys. Soc. Jpn. 63

1994

Earlier work this paper cites.

M. W. Long et al

2003

Earlier work this paper cites.

T. Morimae, A. Sugita, A. Shimizu, Phys. Rev. A71

2005

Earlier work this paper cites.

A. Sugita and A. Shimizu, J. Phys. Soc. Jpn. 74

2005

Earlier work this paper cites.

S. Popescu, A.J. Short, and A. Winter, Nature Phys. 2

2006

Cited alongside, same era.

S. Goldstein et al

2006

Cited alongside, same era.

A. Sugita, RIMS Kokyuroku (Kyoto) 1507

2006

Cited alongside, same era.

P. Reimann, Phys. Rev. Lett. 99

2007

Cited alongside, same era.

Entropy could be obtained if one could obtain a TPQ state of a huge system which includes the target system. However, this is harder than calculating the partition function

Cited in the paper.

These are the conditions that the Boltzmann formula gives the correct thermodynamic entropy and that the system is stable. Hence, they are necessary for all microscopic models to which statistical mechanics is applied

Cited in the paper.

When A ^ \hat{A} is unbounded, ‖ A ^ ‖ \|\hat{A}\| should be replaced with max | ϕ ⟩ ∈ ℋ N ⊂ ⁡ | ⟨ ϕ | A ^ | ϕ ⟩ | \max_{|\phi\rangle\in\mathcal{H}_{N}^{\subset}}|\langle\phi|\hat{A}|\phi\rangle| , where ℋ N ⊂ \mathcal{H}_{N}^{\subset} denotes a Hilbert subspace in which the values of macroscopic variables (such as u u and m z m_{z} ) are limited to certain finite ranges

Cited in the paper.

K. Sakai, private communication

Cited in the paper.

A. Shimizu, J. Phys. Soc. Jpn. 77

2008

Later among the works it cites.

S. R. White, Phys. Rev. Lett. 102

2009

Later among the works it cites.

S. Sugiura and A. Shimizu, Proc. Meeting of Phys. Soc. Jpn. 2011, paper number 23aGA-6

2011

Closest in time.

J. Sato et al

2011

Closest in time.