A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis: Chaotic Systems and Holography

The strong eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration. Although it is expected to hold in a wide class of highly chaotic theories, there are only a few analytic examples demonstrating the strong ETH in special cases, often through methods related to integrability. In this talk, I will explore sufficient conditions for the strong ETH that may apply to a broad range of chaotic theories. These conditions are expressed as inequalities involving the long-time averages of real-time thermal correlators. Specifically, I will discuss bottom-up holographic models that satisfy these conditions under certain assumptions, which are expected to hold in such models. This talk is based on the preprint 2411.09746 [hep-th].