The law of thermodynamics you’re referring to is in a closed system. In this case, energy is being introduced by the burning gasoline pushing the pistons, and a

The law of thermodynamics you’re referring to is in a closed system. In this case, energy is being introduced by the burning gasoline pushing the pistons, and as a byproduct of that, exhaust gases are vented at a certain speed and volume. That is wasted energy as it just goes out the tailpipe more forcefully which adds minimal forward momentum to the car. The reason turbos work is not because they are forcing more air, it’s because they are forcing more air which ALSO raises the compression ratio and the amount of fuel detonating (the MAF will sense the increased air density and add additional fuel to compensate). I.E. a turbo burns more fuel and therefore it produces more power. Hot air is less dense than cold air (why heat rises). Probably keeping the hot side of the turbo hot helps with gas expansion, perhaps that increases the force on the turbine? I’m not sure about that. But the intercooler is to cool the air on the compression side because cold air is denser. Which means more air into the cylinder, which means more fuel. Probably the colder air helps with auto detonation too which lets you push the compression ratio further if the pistons and cylinders can handle it.