Unitarity, ergodicity, and quantum thermodynamics

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.

8 pages

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• Quantum coarse-grained entropy and thermalization in closed systems
• Work and entropy production in generalised Gibbs ensembles
• Emergence of canonical ensembles from pure quantum states
• Dynamics of thermalisation in small Hubbard-model systems
• The quantum cat map on the modular discretization of extremal black hole horizons
• Note on exponential families of distributions
• Comment on "Typicality for Generalized Microcanonical Ensemble"
• Quantum ergodicity for a class of non-generic systems
• Signatures of Anderson localization and delocalized random quantum states