The foundations of statistical mechanics from entanglement: Individual states vs. averages

Abstract

We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.

12 pages, v3 title changed, v2 minor changes

References in corpus (11)

• Average Entropy of a Subsystem
• The capacity of the noisy quantum channel
• Canonical Typicality
• Quantum information can be negative
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Aspects of generic entanglement
• Average Entropy of a Subsystem
• Statistical properties of random density matrices
• Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
• Fourier's Law from Schroedinger Dynamics
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• Classical route to ergodicity and scarring in collective quantum systems
• Quantum computing for classical problems: Variational Quantum Eigensolver for activated processes
• Initial-state-dependent thermalization in open qubits
• Entanglement preserving local thermalization
• Splitting a critical spin chain
• Kinetics of interactions of matter, antimatter and radiation consistent with antisymmetric (CPT-invariant) thermodynamics
• Strong Coupling and non-Markovian Effects in the Statistical Notion of Temperature
• Entanglement in Weisskopf-Wigner theory of atomic decay in free space
• Long-time relaxation of a finite spin bath linearly coupled to a qubit
• Irreversible decoherence of dipole interacting nuclear spins coupled with a phonon bath
• On the foundations of statistical mechanics
• Noise suppression by quantum control before and after the noise
• Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis
• Typical, finite baths as a means of exact simulation of open quantum systems
• Concentration-of-measure theory for structures and fluctuations of waves
• Saturation of entropy production in quantum many-body systems
• Simple scheme for extracting work with a single bath
• Quantum Entropy
• Stability of Quantum Statistical Ensembles with Respect to Local Measurements
• Canonical Typicality For Other Ensembles Than Micro-Canonical
• Out-of-equilibrium quantum thermodynamics in the Bloch sphere: temperature and internal entropy production
• Towards realization of universal quantum teleportation using weak measurements
• Universal Property of Quantum Measurements of Equilibrium Fluctuations and Violation of Fluctuation-Dissipation Theorem
• Ensemble dependence of information-theoretic contributions to the entropy production
• Quantum irreversible decoherence behaviour in open quantum systems with few degrees of freedom. Application to 1H NMR reversion experiments in nematic liquid crystals
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Photon distribution at the output of a beam splitter for imbalanced input states
• Typical Pure Nonequilibrium Steady States
• Microscopic reversibility of quantum open systems
• Second law of thermodynamics with quantum memory
• Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length
• Small violations of full correlation Bell inequalities for multipartite pure random states
• Quantum thermalization and equilibrium state with multiple temperatures
• Structure of the Hamiltonian of mean force
• Full expectation value statistics for randomly sampled pure states in high-dimensional quantum systems
• Hidden thermal structure in Fock space
• Bounding the resources for thermalizing many-body localized systems
• An alternative to the conventional micro-canonical ensemble
• Some no-go results in Quantum Thermodynamics
• Nonequilibrium dynamics of spin-orbit coupled lattice bosons
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• The black hole information paradox and macroscopic superpositions
• Mesoscopic fluctuations in entanglement dynamics
• Scaling functions for eigenstate entanglement crossovers in harmonic lattices
• Nonlocality of Deep Thermalization
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Entropic distinguishability of quantum fields in phase space
• Statistical ensembles without typicality
• Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement
• Quantum Typicality and Initial Conditions
• Local random quantum circuits: ensemble CP maps and swap algebras
• Spin Entropy
• Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
• Time Dependent Quantum Thermodynamics of a Coupled Quantum Oscillator System in a Small Thermal Environment
• Relaxation to equilibrium of expectation values in macroscopic quantum systems
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Allowed and Forbidden Bipartite Correlations from Thermal States
• Quantum ergodicity for a class of non-generic systems
• Closeness of the reduced density matrix of an interacting small system to the Gibbs state
• Simulating quantum thermodynamics of a finite system and bath with variable temperature
• Stiffness of Probability Distributions of Work and Jarzynski Relation for Initial Microcanonical and Energy Eigenstates
• Macroscopic Superposition States in Isolated Quantum Systems
• Canonical density matrices from eigenstates of mixed systems
• Topologically ordered time crystals
• Entanglement production by the magnetic dipolar interaction dynamics
• Entropic bounds between two thermal equilibrium states
• Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
• Total correlations as fully additive entanglement monotones
• Unpacking Black Hole Complementarity
• Long-time equilibration can determine transient thermality
• Symmetry classification of typical quantum entanglement
• Observation of Quantum Equilibration in Dilute Bose Gases
• Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo
• Open-system eigenstate thermalization in a noninteracting integrable model
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Pilot-wave quantum theory with a single Bohm's trajectory
• The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace
• Non-Markovian Equilibration Controlled by Symmetry Breaking
• Increasing complexity with quantum physics
• Bounds on mixed state entanglement
• The Minimal Modal Interpretation of Quantum Theory
• Generic pure quantum states as steady states of quasi-local dissipative dynamics
• Nontrivial damping of quantum many-body dynamics
• Random pure Gaussian states and Hawking radiation
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Matchgate circuits deeply thermalize
• Eigenstate Thermalisation on Average
• The Quantum State of Classical Matter II: Thermodynamic Equilibrium and Hydrodynamics
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement
• Diffusive lossless energy and coherence transfer by noisy coupling
• Study of Open Systems with Molecules in Isotropic Liquids
• Entangling power, gate typicality, and measurement-induced phase transitions
• Localizable quantum coherence
• Non-Clifford Cost of Random Unitaries
• Typical equilibrium state of an embedded quantum system
• Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer
• Correlations in local measurements and entanglement in many-body systems
• Typical pure nonequilibrium steady states and irreversibility for quantum transports
• The Boltzmann distribution and the quantum-classical correspondence
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Clocks and Relationalism in the Thermal Time Hypothesis
• Theory of temporal fluctuations in isolated quantum systems
• Reviving product states in the disordered Heisenberg chain
• Operational derivation of Maxwell-Boltzmann distribution with Maxwell's demon model
• Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis
• How two spins can thermalize a third spin
• Counting atypical black hole microstates from entanglement wedges
• Equilibration and "Thermalization'' in the Adapted Caldeira-Leggett model
• Localization by entanglement
• Generic Entanglement Entropy for Quantum States with Symmetry
• Key Observable for Linear Thermalization
• Microscopic Reversibility and Macroscopic Irreversibility: From a viewpoint of Algorithmic Randomness
• Uncovering Quantum Many-body Scars with Quantum Machine Learning
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate
• Role of correlations in the thermalization of quantum systems
• Typical thermalization of low-entanglement states
• Post quench entropy growth in a chiral clock model
• Thermal states of random quantum many-body systems
• Interference in a two-mode Bose system with $N$ particles is typical
• Correlation in fermion or boson systems as the minimum of entropy relative to all free states
• Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework
• Decoding general error correcting codes and the role of complementarity
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• The Interplay between Frustration and Entanglement in Many-Body Systems
• Confounder Detection in High Dimensional Linear Models using First Moments of Spectral Measures
• Non-ergodic states induced by impurity levels in quantum spin chains
• Some speculations about local thermalization of nonequilibrium extended quantum systems
• Variational Microcanonical Estimator
• Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• Architectures and random properties of symplectic quantum circuits
• Boltzmann entropy for quantum field systems
• Dynamical typicality for initial states with a preset measurement statistics of several commuting observables
• Energy bounds for entangled states
• Signatures of Anderson localization and delocalized random quantum states
• Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands
• Thermalisation of a quantum system from first principles
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Properties of thermal quantum states: locality of temperature, decay of correlations, and more
• Trends of information backflow in disordered spin chains
• Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• Entanglement and Irreversibility in the Approach to Thermal Equilibrium
• Quantum thermalization must occur in translation-invariant systems at high temperature
• Spin and the Thermal Equilibrium Distribution of Wave Functions
• On Computational Complexity of Unitary and State Design Properties
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Smooth Crossover Between Weak and Strong Thermalization using Rigorous Bounds on Equilibration of Isolated Systems
• Evidence for simple "arrow of time functions" in closed chaotic quantum systems
• Observing controlled quantum state collapse in a single quantum trajectory of a mechanical oscillator
• Quantum statistical mechanics from a Bohmian perspective
• Partial projected ensembles and spatiotemporal structure of information scrambling
• Quench of symmetry broken ground states
• Quantum walks as thermalizations, with application to fullerene graphs
• Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
• Quantum Generative Training Using Rényi Divergences
• Single-shot work extraction in quantum thermodynamics revisited
• Assessing thermalization and estimating the Hamiltonian with output data only
• Derivation of Bose-Einstein and Fermi-Dirac statistics from quantum mechanics: gauge-theoretical structure
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Integral Fluctuation Theorem for Microcanonical and Pure States
• Thermalization in Quantum Systems: An Emergent Approach
• Typical observables in a two-mode Bose system
• Thermalization of isolated quantum many-body system and the role of entanglement
• Quantum models of classical world
• Statistical quantum operation
• On the Quantum Structure
• Estimating time in quantum chaotic systems and black holes
• Hawking Radiation: A Comparison of Pure-state and Thermal Descriptions
• Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound
• Strong Chaos of Fast Scrambling Yields Order: Emergence of Decoupled Quantum Information Capsules
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Classical periodic trajectories and quantum scars in many-spin systems
• Appearance of Gibbs states in quantum-state tomography
• Approximate 3-designs and partial decomposition of the Clifford group representation using transvections
• Realism-Completeness-Universality interpretation of quantum mechanics
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Sample complexity of matrix product states at finite temperature
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• Quantum statistical gravity: time dilation due to local information in many-body quantum systems
• Simulating typical entanglement with many-body Hamiltonian dynamics
• Optimal Manipulation Of Correlations And Temperature In Quantum Thermodynamics
• The Copenhagen Interpretation Born Again
• Thermalization is typical in large classical and quantum harmonic systems
• Lindblad quantum dynamics from correlation functions of classical spin chains
• A polynomial time algorithm for studying physical observables in chaotic eigenstates
• Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems
• Many-body eigenstate thermalization from one-body quantum chaos: emergent arrow of time
• Equilibration and Typicality in Quantum Processes
• Entropy augmentation through subadditive excess: information theory in irreversible processes
• How and why does statistical mechanics work
• Stalled response near thermal equilibrium in periodically driven systems
• Model Checking Applied to Quantum Physics
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
• On the energetic analysis of autonomous quantum systems
• The second law of thermodynamics at the microscopic scale
• Theorems on Entanglement Typicality in Non-equilibrium Dynamics
• Gaussian work extraction from random Gaussian states is nearly impossible
• Quantum thermalization and average entropy of a subsystem
• Canonical typicality under general quantum channels
• Long-Time Behavior of Typical Pure States from Thermal Equilibrium Ensembles
• Threefold Way for Typical Entanglement
• A Theory of Inaccessible Information
• Quantum entropy thermalization
• Conjugate measurements, equilibration and emergent classicality
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
• Quantifying entanglement in multipartite conditional states of open quantum systems by measurements of their photonic environment
• Similarities and differences of typicality in quantum and classical systems
• Eigenstate thermalization and ensemble equivalence in few-body fermionic systems
• Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system
• Adaptively secure unitary designs with constant non-Clifford cost
• Quadratic Models for Engineered Control of Open Quantum Systems
• Temperature as perturbation in quantum mechanics
• Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos
• The Model of Quantum Thermodynamics From the First Principles: Quantum Halo or Small Environment
• Quantum equilibration of a model system Porphine
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit
• Vacuum electromagnetic field correlations between two moving points
• The Coherent Crooks Equality
• Theoretical study on thermalization in isolated quantum systems
• Dark Information in Black Hole with $\lambda \phi$ Fluid
• A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics
• Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Page Curve of average subsystem entropy
• Necessity of entanglement for the typicality argument in statistical mechanics
• Scalable and fault-tolerant preparation of encoded k-uniform states
• Diagnosing chaos with projected ensembles of process tensors
• Nontrivial damping of magnetization currents in perturbed spin chains
• Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges
• Thermality versus objectivity: can they peacefully coexist?
• Power of photonic states: from quantum computation to cosmology
• Faster randomized partial trace estimation
• Decoherence without decoherence
• Computing partial transposes and related entanglement functions
• Microscopic Origins of Macroscopic Behavior
• Bekenstein bound in the bulk and AdS/CFT
• Observation of strong and weak thermalization in a superconducting quantum processor
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination
• Open Quantum Systems at Low Temperature
• On the effect of decoherence on quantum tunnelling
• Thermalization of Gases: A First Principles Approach
• Spontaneous parametric down conversion with a depleted pump as an analogue for black hole evaporation/particle production
• Quantum Thermodynamic Integrability for Canonical and non-Canonical Statistics
• Quantum statistical ensemble for emissive correlated systems
• Attraction Induced by Mutual Quantum Measurements of Velocity
• Typical Quantum States of the Universe are Observationally Indistinguishable