> Is there a fundamental minimum cost to flipping bits?

Yes:

https://en.wikipedia.org/wiki/Landauer%27s_principle

But modern computers are nowhere near this theoretical limit, nor any of the other limits I mentioned above. Nevertheless, most of heat generated from modern CPUs does come from bits turning on and off. Each transistor is a tiny capacitor, that holds a charge when its ON. When it switches OFF, it dumps that charge down the drain, creating waste heat. This is a limitation of our technolgy, not a fundamental limit of physics.

Could be worse, though; early chips would disipate heat even when they weren't doing anything. CMOS improved this enormously by pairing up "complementary" transistors so current only flows when something changes.

Still, from the universe's point of view, what we consider a super advanced computer is a lot closer to a space heater than anything that pushes up against its computational limits. Consider, for example, that quarks operate on time scales of 10^23 Hz, and the universe is happy to run three of those in every proton in every star in the universe. In fact, it runs 10^24 of them for one CPU, and that same CPU can't even simulate the quarks of one proton in real time.

Let's face it: we're like kids in Minecraft who think it's cool watch a calculation of 2+2 trickle through a redstone computer in a minute, while the GPU is rendering a billion triangles every second to give them that view.