Non-Abelian transport distinguishes three usually equivalent notions of entropy production
arXiv:2305.15480 · doi:10.1103/PRXQuantum.5.030355
Abstract
We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges' noncommutation, we find, breaks the formulae's equivalence. Furthermore, different formulae quantify different physical effects of charges' noncommutation on entropy production. For instance, entropy production can signal contextuality - true nonclassicality - by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.
arXiv comment11 pages (5 figures) + appendices (14 pages)
References in corpus (111)
- Quantum Coherence as a Resource
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Thermodynamic uncertainty relation for biomolecular processes
- Quantum Thermodynamics
- Fundamental limitations for quantum and nano thermodynamics
- Demonstration of a small programmable quantum computer with atomic qubits
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
- Direct Measurement of the Quantum Wavefunction
- The second laws of quantum thermodynamics
- Canonical Typicality
- Dissipation bounds all steady-state current fluctuations
- Colloquium: Understanding Quantum Weak Values: Basics and Applications
- Generalized Gibbs ensemble in integrable lattice models
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Experimental Observation of a Generalized Gibbs Ensemble
- Contextuality for preparations, transformations, and unsharp measurements
- Contextuality supplies the magic for quantum computation
- Breakdown of thermalization in finite one-dimensional systems
- Experimental Comparison of Two Quantum Computing Architectures
- Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
- Irreversible entropy production, from quantum to classical
- Classical and Quantum Fluctuation Theorems for Heat Exchange
- Complex weak values in quantum measurement
- Direct measurement of general quantum states using weak measurement
- Technical advantages for weak value amplification: When less is more
- Anomalous Weak Values Are Proofs of Contextuality
- Direct Measurement of a 27-Dimensional Orbital-Angular-Momentum State Vector
- Thermodynamic uncertainty relations from exchange fluctuation theorems
- Full characterisation of polarisation states of light via direct measurement
- Non-equilibrium quantum fluctuations of work
- Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
- Jarzynski-like equality for the out-of-time-ordered correlator
- Direct measurement of the density matrix of a quantum system
- Thermodynamics of quantum systems with multiple conserved quantities
- The quasiprobability behind the out-of-time-ordered correlator
- Prior information: how to circumvent the standard joint-measurement uncertainty relation
- Quantum Advantage in Postselected Metrology
- The significance of the imaginary part of the weak value
- Weak Values are Interference Phenomena
- Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation
- Entanglement and the Thermodynamic Arrow of Time
- Thermodynamic resource theories, non-commutativity and maximum entropy principles
- Fully quantum fluctuation theorems
- Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
- Quantum fluctuation theorems, contextuality and work quasi-probabilities
- Full distribution of work done on a quantum system for arbitrary initial states
- Compressive Direct Measurement of the Quantum Wave Function
- Entanglement-assisted weak value amplification
- Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
- Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
- Quantum fluctuation theorems beyond two-point measurements
- The second law of quantum thermodynamics as an equality
- Measuring incompatible observables of a single photon
- Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
- Exact uncertainty relations: physical significance
- Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response
- Beyond heat baths: Generalized resource theories for small-scale thermodynamics
- A quasiprobability distribution for heat fluctuations in the quantum regime
- Verschraenkung versus Stosszahlansatz: Disappearance of the Thermodynamic Arrow in a High-Correlation Environment
- Weak-to-strong transition of quantum measurement in a trapped-ion system
- Information erasure without an energy cost
- Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
- The squeezed thermal reservoir as a generalized equilibrium reservoir
- Complex joint probabilities as expressions of determinism in quantum mechanics
- Restrictions on realizable unitary operations imposed by symmetry and locality
- Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
- Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework
- Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
- Fluctuation Theorems for a Quantum Channel
- Conditions tighter than noncommutation needed for nonclassicality
- Pre- and post-selection, weak values, and contextuality
- Non-Abelian eigenstate thermalization hypothesis
- Nonclassical Properties of Coherent States
- On the role of complex phases in the quantum statistics of weak measurements
- Noncommuting conserved quantities in quantum many-body thermalization
- Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
- Beyond heat baths II: Framework for generalized thermodynamic resource theories
- Noncommuting conserved charges in quantum thermodynamics and beyond
- Non-Abelian symmetry can increase entanglement entropy
- Experimental observation of thermalization with noncommuting charges
- Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
- Non-Abelian Quantum Transport and Thermosqueezing Effects
- Entropic uncertainty relations for quantum information scrambling
- Exchange Fluctuation Theorem for correlated quantum systems
- Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks
- Strengthening weak measurements of qubit out-of-time-order correlators
- Compressive Wavefront Sensing with Weak Values
- The first law of general quantum resource theories
- Class of quasiprobability distributions of work and initial quantum coherence
- Sequential measurements of non-commuting observables with quantum controlled interactions
- Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables
- Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling
- Derivation of quantum mechanics from a single fundamental modification of the relations between physical properties
- Strongly measuring qubit quasiprobabilities behind out-of-time-ordered correlators
- Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases
- What is the most general class of quasiprobabilities of work?
- Quantum heat engine operating between thermal and spin reservoirs
- How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics
- Reference frames which separately store non-commuting conserved quantities
- Measuring incompatibility and clustering quantum observables with a quantum switch
- Building all Time Evolutions with Rotationally Invariant Hamiltonians
- Observation of non-classical correlations in sequential measurements of photon polarization
- Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
- Nonequilibrium thermodynamics of quantum coherence beyond linear response
- Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
- Characterizing symmetry-protected thermal equilibrium by work extraction
- Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
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- Properties and Applications of the Kirkwood-Dirac Distribution
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- Interferometry of quantum correlation functions to access quasiprobability distribution of work
- Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
- Thermodynamic Approach to Quantifying Incompatible Instruments
- Snapshotting Quantum Dynamics at Multiple Time Points
- Evidence of genuine quantum effects in nonequilibrium entropy production
- Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario
- Exploring weak value arguments and Bargmann invariants in -level quantum systems through the Majorana symmetric representation
- Complete characterisation of state conversions by work extraction
- Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
- Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
- General quantum resources providing advantages in work-extraction tasks
- Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges
- Markovian heat engine boosted by quantum coherence
- Universal Statistics of Charges Exchanges in Non-Abelian Quantum Transport
- Information-thermodynamic bounds on precision in interacting quantum systems