Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

Abstract

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the min- and the max-relative entropy to the thermal state coincide approximately, this implies the approximately reversible interconvertibility to and from the thermal state with thermal operations and a small source of coherence. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems, as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.

arXiv comment5 pages + references, 2 figures. Short companion paper to our technical paper published today on the arXiv

References in corpus (66)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Quantifying Coherence
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Quantum Resource Theories
• Operational Resource Theory of Coherence
• The role of quantum information in thermodynamics --- a topical review
• Reference frames, superselection rules, and quantum information
• 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
• The Physics and Mathematics of the Second Law of Thermodynamics
• Catalytic Coherence
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• Work extraction and thermodynamics for individual quantum systems
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• The extraction of work from quantum coherence
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Truly work-like work extraction
• Reversible transformations from pure to mixed states, and the unique measure of information
• The quantum capacity of channels with arbitrarily correlated noise
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• The work value of information
• The Minimal Work Cost of Information Processing
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Thermodynamics of quantum systems with multiple conserved quantities
• An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
• A Generalization of Quantum Stein's Lemma
• Finite blocklength converse bounds for quantum channels
• Resource Theory of Coherence - Beyond States
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Using and reusing coherence to realize quantum processes
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist
• Axiomatic relation between thermodynamic and information-theoretic entropies
• Coherence and asymmetry cannot be broadcast
• Heat-Bath Algorithmic Cooling with optimal thermalization strategies
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• The entropy concept for non-equilibrium states
• Generalized Entropies
• Coherence distillation machines are impossible in quantum thermodynamics
• Fundamental work cost of quantum processes
• Large deviations in quantum lattice systems: one-phase region
• Uncertainty relations in implementation of unitary operations
• Beyond heat baths II: Framework for generalized thermodynamic resource theories
• Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
• On the local equivalence between the canonical and the microcanonical distributions for quantum spin systems
• Reverse Test and Characterization of Quantum Relative Entropy
• Quantum Reference Frames and Their Applications to Thermodynamics
• An Ergodic Theorem for the Quantum Relative Entropy
• Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
• Entropy Meters and the Entropy of Non-extensive Systems
• Quantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb
• Quantum Coding Theorems for Arbitrary Sources, Channels and Entanglement Resources
• Quantum thermodynamics with multiple conserved quantities
• Quantum Causal Structure and Quantum Thermodynamics
• Large Deviation implies First and Second Laws of Thermodynamics
• The Shannon-McMillan Theorem for AF $C^{\ast }$-systems
• Smooth entropy in axiomatic thermodynamics
• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution

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