Does it have to be batches?

Can't it be like the reverse of a rocket engine where they use regenerative cooling from the fuel to cool the rocket nozzle, but just in reverse.

Or like they way my grandpa was doing moonshine -- the alcohol vapors pass through a serpentine in a water tank, condense, at the end you obtain alcohol, the water in the tank gets warmer -- instead, heat water coming from the water cooling tank that is preheated by the vapors of water that is condensing in the serpentine pipe.

Unless you ignore energy sources from the environment you cannot exceed 100% efficiency. And that would be incorrect, applying that same standard to photovoltaic panels would result in infinite efficiency. That doesn't make any sense. Edit: Also, when you take heat/energy from a previous step in the process, you also need to account for the energy put into that previous step. In the end that will again be <100%.

As someone else already pointed out, this would be called Coefficient of Performance. Efficiency is clearly defined and cannot exceed 100% without breaking laws of physics. Call it "3.85 times more efficient than before" or something along those lines and it won't sound like a free energy claim.

> applying that same standard to photovoltaic panels would result in infinite efficiency

No it wouldn't. The equivalent for panels would be like... you want to run some number of watts through a diode, and you're using solar panels to collect this power. The diode happens to give off waste light. By aiming this light at your panels, you can recapture most of it back into electricity, and reuse it 2.85 more times.

the full sentence is:

the [..] device can achieve an overall efficiency of 385 percent in converting the energy of sunlight into the energy of water evaporation.

it seems quite clear how the 3.85 ratio is obtained