Provable quantum thermalization without statistical averages

arXiv:2604.02417 · quant-ph, cond-mat.stat-mech, hep-th, math-ph, math.MP, nlin.CD · Submitted 2026-04-02 · Read on arXiv

quant-ph, cond-mat.stat-mech, hep-th, math-ph, math.MP, nlin.CD

Submitted: 2026-04-02

Updated: 2026-09-16

Comments: 28+20 pages; v2: expanded discussion of long-time forecasts

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Core — 45× in this paper · explained in 2 episodes
• Hilbert Space — 28× in this paper · explained in 2 episodes
• Alignment — 15× in this paper · explained in 1 episode
• Unitary Dynamics — 12× in this paper · explained in 2 episodes
• Entanglement — 8× in this paper · explained in 3 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Trace — 7× in this paper · explained in 2 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• Entanglement Entropy — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Circular Unitary Ensemble — 1× in this paper
• Consistency — 1× in this paper · explained in 3 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Operator Entanglement — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Spectral Geometry — 1× in this paper · explained in 2 episodes

Sources

• The Complexity of Thermalization in Finite Quantum Systems
• Out-of-time-order correlators and quantum chaos
• Science of Chaos or Chaos in Science?
• Boltzmann's Approach to Statistical Mechanics
• Microscopic Origins of Macroscopic Behavior
• Aperiodicity is sufficient for macroscopic thermalization
• Quantum Ergodicity and Mixing
• Scrambling in Double-Scaled SYK and De Sitter Space
• Efficient decoding for the Hayden-Preskill protocol
• Weingarten Calculus
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Interferometric Approach to Probing Fast Scrambling
• On the positivity of Fourier transforms

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