Hybrid cars may have a useful lesson to teach, second stage recovery III

Hybrid cars use regenerative braking in order to recharge their batteries. Could this principle have other applications? With respect to making rockets fully reusable, could the heat energy from reentry be used for some useful purpose? The idea I had, which may or may not be practical, is to use that heat in an active cooling system.

How would this work? Here are a couple ideas in the roughest form. I haven't had time to refine this, so please excuse this if it is impractical or full of errors. I wrote it last night just prior to retiring for the evening.

I wonder what would happen if you were to somehow use the heat of reentry for thrust. Set up a heat exchanger and run some reaction mass through the heat exchanger and send the hot gas out a nozzle for thrust. Would that be feasible?

Another idea:

Let's say that you want to harvest the heat generated by reentry for running a cryogenic cooler which in turn cools the heat shield. The heat shield provides energy for a Stirling engine, which is attached to another Stirling engine in reverse.

A Stirling engine in reverse is a cryogenic device, which can take the hot side of the energy generator and make it cold again. The cold side feeds back into the energy generator's cold side. This will cycle back and forth synergistically providing cooling to the shield, while the shield provides energy for the cooler.

It occurred to me that you could use this on the way up as well. For example, the rocket nozzle needs to be cooled down. Let's say you want to condense some oxygen out of the atmosphere on the way up. You can attach this system to the cooling system of the nozzle so as use that heat for the generation of oxygen by condensation from the cryocooler. The oxygen can be used for thrusting on the way down, or on the way up.

Update:
I am spending some time reading up on the subject. On the subject of reentry during the Apollo Era, I found that the space capsules were designed to produce what is called a "bow shock", which deflected some of the energy away from the craft. It also produced a lot of drag, which was needed to slow down the capsule.

With respect to the idea mentioned above, there has been some study on the concept.  This has led me to a discussion of aerospike engines, but how did I get here?  What does that have to do with reentry?  Puzzling.

I will stop this post here.  Too much detail needs to be mastered.  Frankly, I don't know what I'm doing, so maybe it is best to stop posting about this for now.  Perhaps, after awhile, I will return to it.

Update:

Inflatable heat shields are an intriguing possibility.  I'll have to return to this later.