Clock-work trade-off relation for coherence in quantum thermodynamics

Abstract

In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel insights. Here we describe how thermodynamic coherence splits into two kinds - "internal" coherence that admits an energetic value in terms of thermodynamic work, and "external" coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence we provide dynamical constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clock/work tradeoff relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system.

arXiv comment6 + 10 pages

References in corpus (35)

• Introducing Quantum Discord
• Quantum Coherence as a Resource
• The classical-quantum boundary for correlations: discord and related measures
• The role of quantum information in thermodynamics --- a topical review
• Fundamental limitations for quantum and nano thermodynamics
• A quantum network of clocks
• 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
• Fisher information and multiparticle entanglement
• Multipartite entanglement and high precision metrology
• Catalytic Coherence
• Quantum coherence, time-translation symmetry and thermodynamics
• Work extraction and thermodynamics for individual quantum systems
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Quantum Discord and Maxwell's Demons
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• The extraction of work from quantum coherence
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• An improved Landauer Principle with finite-size corrections
• Extractable Work from Correlations
• A quantum-mechanical Maxwell's demon
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• The Minimal Work Cost of Information Processing
• Metric adjusted skew information
• Measures of macroscopicity for quantum spin systems
• Generalized Laws of Thermodynamics in the Presence of Correlations
• Heat engine driven by purely quantum information
• Thermodynamic cost of creating correlations
• Stochastic independence as a resource in small-scale thermodynamics
• Axiomatic relation between thermodynamic and information-theoretic entropies
• Second laws under control restrictions
• Quantum macroscopicity versus distillation of macroscopic superpositions
• Coherence, Asymmetry, and Quantum Macroscopicity

Cited by in corpus (45)

• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• An introductory review of the resource theory approach to thermodynamics
• Entanglement, coherence and charging process of quantum batteries
• Ergotropy from coherences in an open quantum system
• Quantum battery based on quantum discord at room temperature
• Fluctuation Theorems for a Quantum Channel
• Role of quantum coherence in the thermodynamics of energy transfer
• Energy storage and coherence in closed and open quantum batteries
• Correlations as a resource in quantum thermodynamics
• Coherence distillation machines are impossible in quantum thermodynamics
• Coherence, Quantum Fisher Information, Superradiance and Entanglement are Interconvertible Resources
• Quantifying coherence with respect to general quantum measurements
• Non-Abelian Quantum Transport and Thermosqueezing Effects
• Effects of Quantum Coherence on Work Statistics
• Apparent temperature: demystifying the relation between quantum coherence, correlations, and heat flows
• Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• Measurement Induced Synthesis of Coherent Quantum Batteries
• The first law of general quantum resource theories
• All states are universal catalysts in quantum thermodynamics
• Energetic footprints of irreversibility in the quantum regime
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Engineering a heat engine purely driven by quantum coherence
• Classical and Nonclassical Time Dilation for Quantum Clocks
• Amplifying asymmetry with correlated catalysts
• Key Issues Review: Useful autonomous quantum machines
• Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries
• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Time as a Consequence of Internal Coherence
• Nonequilibrium thermodynamics of quantum coherence beyond linear response
• Second law of thermodynamics for batteries with vacuum state
• Quantifying resources for Page-Wootters mechanism: Shared asymmetry as relative entropy of entanglement
• Demonstrating Quantum Microscopic Reversibility Using Coherent States of Light
• The entropy production of thermal operations
• Quantum thermodynamics with multiple conserved quantities
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• The Duality in Quantum Work
• Quantum coherence assisted dynamical phase transition
• Evidence of genuine quantum effects in nonequilibrium entropy production
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Coherent control of levitated nanoparticles via dipole-dipole interaction
• Complete characterisation of state conversions by work extraction
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
• General quantum resources providing advantages in work-extraction tasks
• Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics