Miniatures on Open Quantum Systems

• URL: http://arxiv.org/abs/2601.20373v1
• Date: Wed, 28 Jan 2026 08:35:57 GMT
• Title: Miniatures on Open Quantum Systems
• Authors: Jan Derezinski, Vojkan Jaksic, Claude-Alain Pillet,
• Abstract summary: The manuscript consolidates and extends a series of invited articles originally prepared for the Modern Encyclopedia of Mathematical Physics.<n>The paper reviews quantum dynamical systems, KMS states, and Tomita-Takesaki modular theory, as well as CCR and CAR algebras for bosonic and fermionic systems.<n>The later sections develop a systematic treatment of small systems coupled to reservoirs, open lattice quantum spin systems, culminating in a detailed discussion of competing notions of quantum entropy production.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We presents a unified and concise exposition of key topics in the mathematical theory of open quantum systems, developed within the framework of operator algebras. The manuscript consolidates and extends a series of invited articles originally prepared for the Modern Encyclopedia of Mathematical Physics, combining foundational material with modern perspectives on non-equilibrium quantum statistical mechanics. After introducing the C*- and W*-algebraic formulation of quantum mechanics, the paper reviews quantum dynamical systems, KMS states, and Tomita-Takesaki modular theory, as well as CCR and CAR algebras for bosonic and fermionic systems. Particular emphasis is placed on infinite systems, non-equilibrium steady states, entropy production, and linear response theory. The later sections develop a systematic treatment of small systems coupled to reservoirs, open lattice quantum spin systems, culminating in a detailed discussion of competing notions of quantum entropy production. The presentation highlights structural insights, conceptual clarity, and connections between equilibrium and non-equilibrium phenomena, providing a self-contained reference for researchers and graduate students in mathematical physics.

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