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 $d$.

arXiv comment9 pages, 4 figures. Accompanying paper of arXiv:2111.12130. Published version

References in corpus (40)

• Quantum Thermodynamics
• Fundamental limitations for quantum and nano thermodynamics
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• The second laws of quantum thermodynamics
• Universality of efficiency at maximum power
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Irreversible entropy production, from quantum to classical
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Truly work-like work extraction
• Axioms and uniqueness theorem for Tsallis entropy
• Algorithmic Cooling and Scalable NMR Quantum Computers
• Microscopic diagonal entropy and its connection to basic thermodynamic relations
• Performance bound for quantum absorption refrigerators
• The role of quantum coherence in non-equilibrium entropy production
• Molecular heat pump
• Autonomous quantum thermal machine for generating steady-state entanglement
• Optimal refrigerator
• Work fluctuations in slow processes: quantum signatures and optimal control
• Elementary Thermal Operations
• Limits to catalysis in quantum thermodynamics
• Second laws under control restrictions
• Heat-Bath Algorithmic Cooling with optimal thermalization strategies
• Third Law of Thermodynamics as a Single Inequality
• Universal features in the efficiency of ultra hot quantum Otto engines
• A sufficient set of experimentally implementable thermal operations
• The Asymptotic Cooling of Heat-Bath Algorithmic Cooling
• Davies maps for qubits and qutrits
• Heat-Bath Algorithmic Cooling with correlated qubit-environment interactions
• Achievable polarization for Heat-Bath Algorithmic Cooling
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• Quantum advantage in simulating stochastic processes
• Open system dynamics from thermodynamic compatibility
• From single-shot to general work extraction with bounded fluctuations in work
• Capacity of non-Markovianity to boost the efficiency of molecular switches
• All states are universal catalysts in quantum thermodynamics
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Collective operations can extremely reduce work fluctuations
• Imperfect Thermalizations Allow for Optimal Thermodynamic Processes
• The reaction coordinate mapping in quantum thermodynamics
• Quantum features and signatures of quantum-thermal machines

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