The second law of thermodynamics makes 100% efficiency impossible. The Carnot efficiency is just a measure of how close you can get to 100%.

It must be a slow day on HN for this post of mine to make the front page :)

Is there any way you could explain to the uninformed, like myself, where the energy would leak? Is it impossible to make a 100% isolated sphere? Would radiation or other kind of waves always pass through?

If it was 100% isolated, the heat from the sun would continually increase the internal temperature, which would probably be bad. They're looking for a steady state dyson sphere.

The energy is converted from short wavelength (visble light) to longer wavelengths (infrared). A Dyson sphere would act as a black body [1] and radiates energy at the temperature of the sphere outer surface.

1. https://en.m.wikipedia.org/wiki/Black-body_radiation

The problem with a 100% isolated sphere that you can't dump entropy either.

Energy can't be recycled in that sense. There is a maximum amount of useful work which can be extracted from a given source of energy - this is called the "exergy." Exergy is not conserved. Once all the exergy is gone, it doesn't matter how much energy there is; it can't be moved around or manipulated in any way.

https://en.wikipedia.org/wiki/Exergy

That would be equivalent to a perpetual motion machine, so I don't think it's possible for thermodynamical reasons.

No, because it cannot be 100% efficient. If it were you would have a perpetual motion machine.