Entropy is define as the measure of uncertainty in a system, and more in particular, when talking about information theory, it’s the average number of bits needed to describe or predict something.

Entropy in crypto is often confused with TVL, as in, the bigger the Private Pool (in any of its shapes) the bigger it is its security. And although there’s a correlation between the size of the pool and its entropy, they are not the same thing and the only reason it gives more security is because it’s assumed more people are using it. **And that’s the whole point, you don’t need a big TVL in order to have entropy, you can simply incentivize noise creation. **

Let me add an example: You have a private pool with 100k eth, a user deposits 1 eth, and then in another address the user withdraws that 1 eth. How long the user has to wait until there’s been enough transactions through the same pool for me not being able to identify whether that new 1 eth withdrawal belongs to the user? Because if the user withdraws immediately I’ll know it. It’s all about entropy, noise, and purely tech can’t solve this.

Then, the question becomes how do you make it so users create more transactions? Some protocols like Bermuda and Railgun have landed on executing DeFi through their protocol, that way you achieve higher noise and “private DeFi”. This is very shortsighted, you can’t create a new “module” every time to interact with DeFi, plus then wallets needing to understand that. Privacy should play nicely with design architecture we have in Ethereum, that is, addresses.

But traditional private pools can’t easily do that, because the claiming address needs eth to do the claiming. Who’s sending that initial gas and how’s that not tied to you?
If you solve that, Ephemeral Addresses become real contenders to have proper privacy.

A goose humorously questions a person running away about the source of gas, declaring it neither crustless nor scalable.