I've thought long about this issue before.  Since mining is inherently a futures market, there are many ways you can try to replicate this feature, either with time opportunity costs, or proof of burn combined with strange economic systems.  Most of the methods of trying to do so with time opportunity costs just replicate some form of proof of stake and create another closed entropy, permissioned ledger like all proof of stake coins.  However, you might be able to utilize proof of burn and some weird economic system to combine the two while still being an open entropy, permissionless ledger.

I say "weird economic system" for a reason, because the last time anyone tried making a coin like this was "Slimcoin", and I think people proof of burned half the entire money supply just for the fuck of it.