Resource theory of quantum thermodynamics: Thermal operations and Second Laws

Abstract

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity, and asymmetry. Such frameworks are characterized by two main elements: a set of predefined (free) operations and states, that one assumes to be easily obtained at no cost. Given these ground rules, one can ask: what is achievable by using such free operations and states? This usually results in a set of state transition conditions, that tell us if a particular state $\rho$ may evolve into another state ${\rho }^{\prime }$ via the usage of free operations and states. We shall see in this chapter that thermal interactions can be modelled as a resource theory. The state transition conditions arising out of such a framework, are then referred to as "second laws". We shall also see how such state transition conditions recover classical thermodynamics in the i.i.d. limit. Finally, we discuss how these laws are applied to study fundamental limitations to the performance of quantum heat engines.

arXiv commentBook chapter in 'Thermodynamics in the quantum regime - Recent Progress and Outlook'. 13 pages

References in corpus (66)

• Quantum entanglement
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantifying Coherence
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Time-dependence of correlation functions following a quantum quench
• Operational Resource Theory of Coherence
• 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
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• A nano heat engine beyond the Carnot limit
• Catalytic Coherence
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Quantum coherence, time-translation symmetry and thermodynamics
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• How small can thermal machines be? The smallest possible refrigerator
• The resource theory of quantum reference frames: manipulations and monotones
• The thermodynamic meaning of negative entropy
• Work extraction and thermodynamics for individual quantum systems
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Second law and Landauer principle far from equilibrium
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• Entanglement-assisted local manipulation of pure quantum states
• Non-Gaussian entanglement distillation for continuous variables
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Extractable Work from Correlations
• Truly work-like work extraction
• Reversible transformations from pure to mixed states, and the unique measure of information
• Entanglement enhances cooling in microscopic quantum fridges
• A Resource Framework for Quantum Shannon Theory
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Thermodynamics of quantum systems with multiple conserved quantities
• Finite quantum dissipation: the challenge of obtaining specific heat
• Thermodynamic resource theories, non-commutativity and maximum entropy principles
• Fully quantum fluctuation theorems
• Bidirectional Single-Electron Counting and the Fluctuation Theorem
• Are the laws of entanglement theory thermodynamical?
• Entanglement distillation by dissipation and continuous quantum repeaters
• Markovian Master Equation and Thermodynamics of Two-level System in Strong Laser Field
• Specific heat anomalies of open quantum systems
• The second law of quantum thermodynamics as an equality
• Correlating thermal machines and the second law at the nanoscale
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• Elementary Thermal Operations
• A measure of majorisation emerging from single-shot statistical mechanics
• Thermodynamic work from operational principles
• System-bath entanglement in nanothermodynamics
• Clock-Driven Quantum Thermal Engines
• Fundamental work cost of quantum processes
• Beyond heat baths II: Framework for generalized thermodynamic resource theories
• A sufficient set of experimentally implementable thermal operations
• What is the probability of a thermodynamical transition?
• From single-shot towards general work extraction in a quantum thermodynamic framework
• Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics
• From single-shot to general work extraction with bounded fluctuations in work
• Work and reversibility in quantum thermodynamics
• Surpassing the Carnot Efficiency by extracting imperfect work
• Quantum Reference Frames and Their Applications to Thermodynamics
• Fluctuations in Single-Shot $\epsilon$-Deterministic Work Extraction

Cited by in corpus (9)

• An introductory review of the resource theory approach to thermodynamics
• The maximum efficiency of nano heat engines depends on more than temperature
• All states are universal catalysts in quantum thermodynamics
• The operational significance of the quantum resource theory of Buscemi nonlocality
• The entropy production of thermal operations
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Revising the quantum work fluctuation framework to encompass energy conservation
• Thermal operations from informational equilibrium