Work Extraction from a Single Energy Eigenstate

Abstract

Work extraction from the Gibbs ensemble by a cyclic operation is impossible, as represented by the second law of thermodynamics. On the other hand, the eigenstate thermalization hypothesis (ETH) states that just a single energy eigenstate can describe a thermal equilibrium state. Here we attempt to unify these two perspectives and investigate the second law at the level of individual energy eigenstates, by examining the possibility of extracting work from a single energy eigenstate. Specifically, we performed numerical exact diagonalization of a quench protocol of local Hamiltonians and evaluated the number of work-extractable energy eigenstates. We found that it becomes exactly zero in a finite system size, implying that a positive amount of work cannot be extracted from any energy eigenstate, if one or both of the pre- and the post-quench Hamiltonians are non-integrable. We argue that the mechanism behind this numerical observation is based on the ETH for a non-local observable. Our result implies that quantum chaos, characterized by non-integrability, leads to a stronger version of the second law than the conventional formulation based on the statistical ensembles.

References in corpus (50)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• The large deviation approach to statistical mechanics
• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum many-body systems out of equilibrium
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Experimental Observation of a Generalized Gibbs Ensemble
• On Many-Body Localization for Quantum Spin Chains
• Quantum mechanical evolution towards thermal equilibrium
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Universal dynamics and renormalization in many body localized systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
• Spin-chain model of a many-body quantum battery
• Ergodic dynamics and thermalization in an isolated quantum system
• Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
• Finite-size scaling of eigenstate thermalization
• Does a single eigenstate encode the full Hamiltonian?
• Eigenstate thermalization within isolated spin-chain systems
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Eigenstate thermalization in the two-dimensional transverse field Ising model
• Fluctuation Theorem for Many-Body Pure Quantum States
• Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
• Thermal machines beyond the weak coupling regime
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Work and entropy production in generalised Gibbs ensembles
• On the local equivalence between the canonical and the microcanonical distributions for quantum spin systems
• The Second Law of Thermodynamics under Unitary Evolution and External Operations
• Weak eigenstate thermalization with large deviation bound
• Eigenstate Thermalization Hypothesis and Quantum Jarzynski Relation for Pure Initial States
• Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States
• Work extraction in an isolated quantum lattice system: Grand canonical and generalized Gibbs ensemble predictions
• Saturation of entropy production in quantum many-body systems

Cited by in corpus (12)

• Many-body localized quantum batteries
• Time evolution of correlation functions in quantum many-body systems
• Local passivity and entanglement in shared quantum batteries
• Characterizing symmetry-protected thermal equilibrium by work extraction
• Eigenstate Fluctuation Theorem in the Short and Long Time Regimes
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Scaling at the OTOC Wavefront: free versus chaotic models
• Continuous-time quantum optimisation without the adiabatic principle
• Microscopic Reversibility and Macroscopic Irreversibility: From a viewpoint of Algorithmic Randomness
• The second law of thermodynamics from concavity of energy eigenvalues
• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• The second law of thermodynamics from concave energy in classical mechanics