Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Abstract

The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a new framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization, and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing non-equilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a $\text{Mathematica}$ implementation solving $d=6$ on a laptop computer in minutes.

20 pages, 5 figures. Accompanying paper of arXiv:2202.12616. Published version

References in corpus (4)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Capacity of non-Markovianity to boost the efficiency of molecular switches
• Optimizing thermalizations

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• Entanglement generation from athermality
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• Quantum processes as thermodynamic resources: the role of non-Markovianity
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
• Thermalization of finite complexity and its application to heat bath algorithmic cooling
• Strong symmetries in collision models and physical dilations of covariant quantum maps
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• Cooling and work extraction under memory-assisted Markovian thermal processes
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• Universality and classification of elementary thermal operations