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 (6)

• Canonical Typicality
• Quantum information can be negative
• Aspects of generic entanglement
• Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
• Fourier's Law from Schroedinger Dynamics
• Thermalization of quantum systems by finite baths

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