What's your favourite gear ratio?

It takes less energy to accelerate a 40/13 gear ratio from 0 to 120r.p.m. than it does a 52/17 ratio, that's an undisputed fact.

It's not undisputed, because I dispute it.

We can pretty much disregard the chainring and sprocket inertia, because the difference is tiny next to the inertia of the heavy chain. On the big ring, the chain has to go faster, so you definitely need to add more energy to that system to get it up to speed. However, the big ring system has higher efficiency, you can look up chain drive theory for yourself or you can take my word for it, but it's the case either way.

Now, the pcd of a 52t ring is 210mm, and 120rpm is 4π rad/s, so the eventual chain speed is 0.105×4π m/s, and the chain mass is about 0.4kg, so it's kinetic energy is
0.5×0.4×(0.105×4π)²=0.35J
We can simply scale for the little ring to get (40/52)²×0.35=0.20J

Of course, the big-ring system needs a greater length of chain, by about 12%, and that extra 50g of chain also need to be accelerated with the rest of the bike up to about 15m/s, so there is another 5J of energy to expend there, which swamps the 0.15J difference caused by the higher chain speed.

Now, let's say for the sake of argument we do this acceleration over a period of 10s, the extra power needed to accelerate the big-ring drive is 0.5W. This kind of acceleration needs quite a lot of input power, somewhere in the region of 1000W, and some old calculations I did using some long lost software indicated that the theoretical difference in chain absorbed power at 250W at 100rpm was about 1W when going from 40t to 60t, so we can hazard a reasonably informed guess that you're going to need something like an extra 2W to overcome the extra losses if you drive a 40t rather than a 52t at 1000W.

Feel free to pick holes in my analysis, but at first pass it looks like you could never accelerate fast enough on a bicycle to make the drivetrain inertia matter, because the the excess friction losses are always running away from the tiny decrease in the energy needed to bring the drive up to speed, by a factor of about 4.