ChatGPT is definitely aware that it exists. In humans, the self-referential inner monologue activates when the mind is idle. The Default Mode Network is responsible for that processing. Can it be that ChatGPT is "thinking" when it's idle as well?
Self awareness needs notion of time and self referential memory.
ChatGPT doesn't exist when it's idle.
It's activated when transforming input into next potential token (list of tokens with probabilities).
Ie. it's just sophisticated pure function mapping input -> list of tokens with probabilities.
What's incredible is that it actually works when you keep repeating it.
Notion of thinking time doesn't exist for it. It can for example branch in the middle. You can calculate one token in this data-center, next one on another continent etc.