Optimizing thermalizations

Abstract

We present a rigorous approach, based on the concept of continuous thermomajorisation, to algorithmically characterise the full set of energy occupations of a quantum system accessible from a given initial state through weak interactions with a heat bath. The algorithm can be deployed to solve complex optimization problems in out-of-equilibrium setups and it returns explicit elementary control sequences realizing optimal transformations. We illustrate this by finding optimal protocols in the context of cooling, work extraction and catalysis. The same tools also allow one to quantitatively assess the role played by memory effects in the performance of thermodynamic protocols. We obtained exhaustive solutions on a laptop machine for systems with dimension $d\le 7$, but with heuristic methods one could access much higher $d$.

9 pages, 4 figures. Accompanying paper of arXiv:2111.12130. Published version

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Cited by in corpus (14)

• Catalysis of entanglement and other quantum resources
• Operational definition of the temperature of a quantum state
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Catalysis in Action via Elementary Thermal Operations
• Complete Characterization of Entanglement Embezzlement
• A hierarchy of thermal processes collapses under catalysis
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Lindbladian-Induced Alignment in Quantum Measurements
• Thermalization of finite complexity and its application to heat bath algorithmic cooling
• Majorization requires infinitely many second laws
• Cooling and work extraction under memory-assisted Markovian thermal processes
• Universality and classification of elementary thermal operations
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport