Work and reversibility in quantum thermodynamics

Abstract

It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\rho$ to a final state $\sigma$, and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\rho$ to a thermal state $\sigma$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\sigma$ to its original form $\rho$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition, and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.

14 pages

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Cited by in corpus (18)

• The role of coherence in the non-equilibrium thermodynamics of quantum systems
• Fully quantum fluctuation theorems
• Fluctuation Theorems for a Quantum Channel
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Relative submajorization and its use in quantum resource theories
• Quantum Coherence in a Quantum Heat Engine
• Entanglement Wedge Reconstruction using the Petz Map
• Approximate reversal of quantum Gaussian dynamics
• Quantum Thermodynamics and Quantum Coherence Engines
• Approximate quantum Markov chains
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?
• Resource theory of quantum thermodynamics: Thermal operations and Second Laws
• Optimality Condition for the Petz Map
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• Non-Markovian Quantum Heat Statistics with the Reaction Coordinate Mapping
• Quantum reversal: a general theory of coherent quantum absorbers
• Thermal operations from informational equilibrium