How many transactions (TPS) can Ethereum 2.0 process?

Question

Today, Ethereum has ~15 TPS, transactions per second.

What will Ethereum 2.0 be able to process?

Answer 1

EDIT July 2022: From the EF Research AMA Part 8, Drake writes:

Talking in rough orders of magnitude Ethereum can do 10 TPS today. There are three compounding 100x that would bring us to 10M TPS (enough for 100 transactions per person per day):

• 100x from rollups
• 100x from sharding
• 100x from bandwidth growth over 10 years (Nielsen's law)

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In A rollup-centric ethereum roadmap, Buterin writes:

• If everyone moves to rollups, we will soon have ~3000 TPS.
• Once phase 1 comes along and rollups move to eth2 sharded chains for their data storage, we go up to a theoretical max of ~100000 TPS.
• Eventually, phase 2 will come along, bringing eth2 sharded chains with native computations, which give us… ~1000-5000 TPS.

Rollups have higher TPS as he explains:

It seems very plausible to me that when phase 2 finally comes, essentially no one will care about it. Everyone will have already adapted to a rollup-centric world whether we like it or not, and by that point it will be easier to continue down that path than to try to bring everyone back to the base chain for no clear benefit and a 20-100x reduction in scalability.

But rollups do not weaken Ethereum, which still remains the critical, base layer:

This will help Ethereum distinguish itself as having a stronger security model than other sharded L2 chains, which are all going in the direction of having sharded execution of some form; eth2 would be the base layer that’s just powerful enough to have functionality escape velocity, and no more powerful.