> One of those pesky laws of thermodynamics seems to imply that if a turbo only used the kinetic energy of the exhaust it would not be able to overcome the losses of transferring the energy into the intake and would be a net drain on power.

Turbos aren't really about transferring energy into the intake. It's about getting more air (oxygen) into the intake, so you can burn more fuel per engine stroke. The extra power comes from combusting more inputs.