SEMINAR 2025

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 irreversible entropy growth dictated by the second law of thermodynamics. Despite its ubiquity and conceptual significance, a complete proof of quantum thermalization has remained elusive for several decades. Here, we prove that quantum thermalization must occur in any qubit system with local interactions satisfying 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. Time permitting, I will talk about extensions of our proof to thermalization to generalized Gibbs states in systems with additional conserved quantities.

Based on: https://arxiv.org/abs/2409.07516