Decomposable coherence and quantum fluctuation relations

Abstract

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process', and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable' and `non-decomposable' quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.

40 pages, 7 figures, accepted by Quantum

References in corpus (42)

• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Operational Resource Theory of Coherence
• Fluctuation theorems: Work is not an observable
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Multipartite entanglement and high precision metrology
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Contextuality in Measurement-based Quantum Computation
• Multipartite entanglement in spin chains
• Information processing and the second law of thermodynamics: an inclusive, Hamiltonian approach
• No-go theorem for the characterisation of work fluctuations in coherent quantum systems
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• The completeness of quantum theory for predicting measurement outcomes
• Quasi-quantization: classical statistical theories with an epistemic restriction
• Quantum from principles
• Non-equilibrium quantum fluctuations of work
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• Jarzynski-like equality for the out-of-time-ordered correlator
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Quantum Operation Time Reversal
• Fully quantum fluctuation theorems
• Fluctuation theorems for quantum processes
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• The WAY theorem and the quantum resource theory of asymmetry
• The second law of quantum thermodynamics as an equality
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• Wigner-Yanase skew information as tests for quantum entanglement
• Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework
• The asymmetry properties of pure quantum states
• Generalized canonical ensembles and ensemble equivalence
• Fluctuation Theorems for a Quantum Channel
• No Return to Classical Reality
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Measurement-dependent corrections to work distributions arising from quantum coherences
• Alignment of reference frames and an operational interpretation for the G-asymmetry
• Theory of Josephson Photomultipliers: Optimal Working Conditions and Back Action
• An autonomous quantum machine to measure the thermodynamic arrow of time
• Coherent fluctuation relations: from the abstract to the concrete
• Strong Converse and Stein's Lemma in the Quantum Hypothesis Testing
• Quantum coherence fluctuation relations
• The role of quantum work statistics in many-body physics
• Photon-added and photon-subtracted coherent states on a sphere

Cited by in corpus (8)

• Quantum work statistics close to equilibrium
• The role of quantum coherence in energy fluctuations
• The First Law of Quantum Field Thermodynamics
• Thermodynamics of relativistic quantum fields confined in cavities
• Catalytic Gaussian thermal operations
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Quantifying athermality and quantum induced deviations from classical fluctuation relations
• Quantum fluctuation theorem for initial near-equilibrium system