Based on the laws of thermodynamics, shouldn't it be theoretically impossible for a non plug-in hybrid vehicle to ever be more fuel-efficient than a vehicle that connects the same engine directly to the wheels without converting it into electricity first?
The only energy input on a non plug-in hybrid is the gas tank, and therefore any energy leaving the vehicle in the form of torque must have originated in that tank. When the vehicle is driven, electrical energy leaves the battery and is converted into kinetic energy by the motors.
Once the battery is depleted, the gasoline engine begins turning, converting chemical energy into kinetic energy, which turns the wheels directly as well as turning an alternator which converts the kinetic energy into electrical energy, charging the battery.
But since all this energy is, no matter what, coming from that gas tank, it really doesn't matter what form it's in when it's turned towards moving the vehicle; it still started out as the same amount of chemical energy!
Furthermore, no conversion of energy can ever be one hundred percent efficient: some is inevitably lost to heat and other forms of unusable energy. So chemical -> kinetic -> electrical -> kinetic will always be less efficient than chemical -> kinetic.
The only ways I can think of a hybrid being more efficient is through energy recovery; the regenerative breaking system turns kinetic energy back into electrical instead of turning it into heat and wasting it like in normal brakes. But will the energy recovered by this method ever be greater than the energy lost by the extra conversions, as well as the increase inertia from the heavy components?