Quantum thermalization must occur in translation-invariant systems at high temperature
arXiv:2409.07516 · doi:10.1038/s41467-025-66777-7
Abstract
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schrödinger's equation and the second law of thermodynamics. Despite its ubiquity and conceptual significance, the precise conditions that give rise to quantum thermalization are still not well understood. After nearly a century of efforts, we have yet to find a complete mathematical proof that an effective statistical description naturally emerges the underlying quantum dynamics in generic settings. Here, we prove that quantum thermalization must occur in any qubit system with local interactions under three conditions: (i) high effective temperature, (ii) translation invariance, and (iii) no perfect resonances in the energy spectrum. Specifically, we show that a typical, low-complexity pure state drawn from any ensemble with large entropy and well-defined effective temperature becomes locally indistinguishable from a Gibbs state upon unitary evolution. In this setting, our rigorous results prove the widely anticipated notion that statistical physics should be understood as an emergent phenomenon, explicitly derived from the first principles of quantum mechanics.
8 pages, 3 figures, 20 page supplement. New results for low-complexity initial states and generalized Gibbs states. New title
References in corpus (43)
- 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
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Many-body localization, thermalization, and entanglement
- Quantum thermalization through entanglement in an isolated many-body system
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Canonical Typicality
- Generalized Gibbs ensemble in integrable lattice models
- Experimental Observation of a Generalized Gibbs Ensemble
- Quantum mechanical evolution towards thermal equilibrium
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Localization from Hilbert space shattering: from theory to physical realizations
- Local constraints can globally shatter Hilbert space: a new route to quantum information protection
- Jerusalem Lectures on Black Holes and Quantum Information
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Quantum equilibration in finite time
- Quantum memories at finite temperature
- QCD thermalization: Ab initio approaches and interdisciplinary connections
- Thermal Fluctuations in Quantized Chaotic Systems
- Subsystem ETH
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- Typical fast thermalization processes in closed many-body systems
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Spectra and eigenstates of spin chain Hamiltonians
- Lectures on the Bethe Ansatz
- Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems
- Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains
- Time evolution of correlation functions in quantum many-body systems
- Thermalization under randomized local Hamiltonians
- Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems
- Quantum many-body systems in thermal equilibrium
- Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interaction
- Extensive entropy from unitary evolution
- Typical thermalization of low-entanglement states