Does ETH Always Lead to Thermalization?

The Eigenstate Thermalization Hypothesis (ETH) is a big topic in the world of physics. One common way to think about ETH suggests it might not always mean that an observable in an isolated quantum system made up of many bodies will thermalize. To get thermalization, you might need to assume a specific distribution, like the canonical or microcanonical one, in the ETH framework. More generally, you can assume other averages in a more flexible ETH framework, which could lead to different equilibrium conditions.

ETH isn't just about thermalization. Thinking about it can open up new ways to understand how systems behave over time. It's like wondering why a hot cup of coffee cools down. ETH helps explain how energy spreads out and our system reaches a stable state. But it's not always a sure thing. Sometimes, we need to think beyond the usual assumptions to truly understand what's happening.

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