I meant the working fluid i.e nitrogen.

The big disadvantage right now is the cost of creating it.
The use of stirling engines help and as I said I'm investigating using hirsch vortex tubes. There are also acoustic refrigeration. Needless to say efficient condensation of gasses is not and area that has recieved a huge amount of research since regular compressors work well even though there not efficient. You can use other working fluids the only real requirment is the boiling point is lower then room temperature. The energy is from the phase change liquid->gas.

Hmm. I looked at your site. You'll still run into some laws of thermodynamics. Extracting useful work from a temperature difference is always going to be less than 100% efficient.

And the cost of LN2 is almost entirely the cost of the energy to produce it.

If I had the money, time, and patience to build an energy storage system in my garage, I'd go with nickel-iron batteries. Your energy out / energy in is only about 40% but they last forever, have no moving parts, and are beautifully low-tech.

I thought a lot about batteries but they don't seem to provide the load response that a thermodynamic system can. LNG is also potentially a good choice but again with liquid nitrogen you don't care about the working fluid. Both work well for the major peak load problem air conditioning since the effectively replace that use case via cooling the air using a stored refrigerant. Current refrigerants are also a good possibility I'd say freon but it not freon any more. The problem with anything not liquid nitrogen is you have to store the gas till you compress again which is why I chose liquid nitrogen since you can exhaust to the atmosphere.