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arXiv · quant-ph/0702009

Unitarity, ergodicity, and quantum thermodynamics

Dorje C. Brody·Daniel W. Hook·Lane P. Hughston
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Abstract

This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand canonical density matrix involving a complete commuting set of observables including the Hamiltonian. The result obtained, which is derived for a generic finite-dimensional quantum system, shows that the equilibrium state arising from unitary evolution is always expressible in the canonical form, without the consideration of a system-bath decomposition.

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Dorje C. Brody, Daniel W. Hook, Lane P. Hughston. 2007-06-13. Unitarity, ergodicity, and quantum thermodynamics. https://doi.org/10.1088/1751-8113/40/26/f01

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