How are new coins minted in Proof of Stake systems I've been trying to understand Proof Of Stake cryptocurrency systems, but I don't see how new coins are made using the Proof Of Stake system.
My current understanding of Proof Of Stake

People put up a certain amount of cryptocurrency they already hold for a chance to be the entity that creates the next block.  This is the Stake.

Whoever is chosen to write the next block verifies the transactions and as a reward gets to keep all the transaction fees.  If you're not chosen, you get your Stake back.

The Stake of the new block writer is held in escrow (i.e. not allowed to be spent) until several new blocks are added.

If they are found to be cheating they loose their Stake.


I don't see where new coins are being added.  It seems like the coin supply is set and it just moves around as people pay transaction fees.
In Bitcoin, and other Proof Of Work systems, I would buy a computer and become a miner.  I'd keep solving hash problems until I mined a coin, then I could spend the coin.  I do not need to have Bitcoin to mine it.  With Proof of Stake it appears I have to have currency to get more - it's a chicken and egg problem.
In a Proof Of Stake system, how do I go from 0 coins to 1 coin?  For example, I invent a Proof Of Stake cryptocurrency.  How do people besides me get coins to spend?
In a purely Proof-Of-Stake cryptocurrency the number of coins is fixed
And so are most government back currencies.  Interest in Proof-Of-Stake seems to be driven by the rise of 51% attacks, Ethereum Classic has been attacked multiple times, which significantly drove down value.
Unless you're BitCoin, the network of miners is simply not big enough to protect your blockchain once your coins start getting valuable.  Each Ethereum coin is worth about $1,500, which is enticing for attackers.  You can hoard coins, spend thousands on a 51% attack and still come out ahead.
Because of repeated 51% attacks, Ethereum released Ethereum 2.0, which swapped from a Proof-Of-Work, like BitCoin, to Proof-Of-Stake.  There were already plenty of coins and a healthy user base, so not adding new coins wasn't that big a deal.
By switching to Proof-Of-Stake Ethereum 2.0 forces any attacker to put up coins they won't get back quickly.  51% attacks work by overwhelming the network for a short time and cashing out.  Now any attacker would have to control 51% of the network for a long time in order to cheat and get the Stake back.
But where do the Proof-of-Stake coins come from
Ethereum started as a Proof-of-Work cryptocurrency and swapped over to Proof-of-Stake to stop attacks.  Most of the Proof-Of-Stake cryptocurrencies started out as Proof-Of-Work then switched over to Proof-Of-Stake after they had plenty of coins to go around and a good eco-system of users.
Proof-Of-Stake is a way for smaller cryptocurrencies to protect their blockchains.  BitCoin doesn't have to worry as much about a 51% attack since it is the largest cryptocurrency by far.  For reference each BitCoin is worth 48,850 USD while each Ethereum coin is worth 1,500 USD.
How I figured this out
Reading and re-reading the Ethereum 2.0 website
This reddit thread ask a similar question, which lead me to this article.