Unitarity, Ergodicity and Quantum Thermodynamics

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Brody, D C; Hook, D W and Hughston, L P. 2007. Unitarity, Ergodicity and Quantum Thermodynamics. Journal of Physics A: Mathematical and Theoretical, 40(26), F503-F509. ISSN 1751-8113 [Article]

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Official URL: https://doi.org/10.1088/1751-8113/40/26/F01

Abstract or Description

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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Article

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https://doi.org/10.1088/1751-8113/40/26/F01