Pure Information Gives Off Heat

I do have a degree in computer science and I find you again and again to be one of my best CS teachers in topics, that were never discussed or badly explained during my studies!

Fun fact: Reversible logic is really important in quantum computing. Since all state changes can be represented as unitary matrices, quantum gates are always reversible.

Jade, your ability to explain complex quantitative concepts so clearly is exceptional. We need more teachers like you.

I worked in the semiconductor industry (DRAM) for a few years and now one of the courses I teach is Thermodynamics. I had no idea about the Landauer limit so thanks for teaching me something new! Also, good work pointing out that a completely reversible process is not possible as there is always some energy loss (collisions in your billiard ball case). This was an excellent video!

I love Jades vibe of having a secret to share

Good stuff! If you're interested there's an even weirder (and very theoretical) application of reversible computing called a "Szilard engine" where you can go back and forth between waste data and waste energy. Using the wasted bits of reversible computing you can theoretically extract energy out of a system that's at an equilibrium state, basically meaning you can convert energy into data and data into energy

While the second law gives a mathematical justification for that energy loss, it does not give a deeper "why" that is the case. The fundamental issue is that of information erasure itself. This comes down to collapsing a state to a single value. Imagine the 2 bits getting reduced to 1 bit. This means we force one bit from having a variable state (either 0 or 1) to a fixed state. It can be any value, does not matter, but it is now a constant and no longer a variable. This is where the loss occures. One helpful visual is a ball in a potential with 2 valleys (as a standin for a particle in a bipotential). Now this ball can be in either of the 2 valleys initially. By definition we dont know, else it would be a known constant and not a variable. Lets say we want to move this ball into the left valley, from any starting valley. The issue here is that whatever we come up with needs to work for both starting valleys. Similar the bit erasure must be able to set a 0 to a 0, but also a 1 to a 0. In the ball case, you can move it over to the other valley but then it will have some speed left, which you need to dissipate in order for it to come to a rest at the bottom and keep this state. This is exactly where the loss happens. You can add some kind of reversible damping to "catch" this energy, but then it wont work for the case that the ball was already in the correct valley. Whatver case you design it for will always cause an energy loss for the other case, since you need to move from a case with potentially "some" kinetic energy to a state with "zero" kinetic energy, without knowing the direction of the motion. (This is similar to maxwells demon). Now how much energy do we need to dissipate? Also easy to see. In order to differentiate between the 2 bit states, there needs to be a potential barrier between them. This barrier needs to be high enough to prevent thermal movement from flipping the bit on its own. The energy you need to dissipate while "catching" the bit and bringing it to rest is directly coming from the energy you need to expend to cross this barrier. Since the barrier is temperature related (more temperature -> more thermal energy -> higher barrier needed to avoid flips), the energy loss is also temperature dependent. This is where the "T" in the equation comes from. The boltzman constant in a way is mandatory to match the units. Last piece of the puzzle is the ln(2). We can either be satisfied with using the second law as a shortcut here, but the ln(2) can also be derived directly from the "geometry" of this "information bit in 2 potential wells" problem.

This has become my favorite YouTube channel. These short, digestible discussions of deep topics. Are endlessly fascinating. I especially enjoy the discussions of paradoxes. Also, you are amgreat presenter - clear and engaging. Keep itn up, please!❤

This took me back to my statistical physics classes! Wonderfully explained! Thank you so much!

Amazing to think about. I spent 10 years designing actual microprocessors and always thought of energy in terms of the electrical current flowing through the device.

I was wondering about the "many million more" at 10:00 and did some math as I thought this sounded a little too much. But turns out it's about right: A somewhat modern 64bit x86 CPU has around 5*10^8 logic gates. Let's say with each cycle 1% of those gates gets flipped and there are 2*10^9 cycles per second (2GHz), then we end up with around 1µW. Modern power efficient x86 processors need roughly 10W, which is 10 million times this. Not sure what the numbers are like with an ARM processor in a smartphone. Of course this is just ballpark-math.

im just a stupid highschool dropout but to me it seems all of these energies are really kinetic energy. whether it moves a car, or manipulates information or produces heat, if you zoom in you move atoms in a way that benefits you, you move atoms to move the car=kinetic, you move atoms/electrons/photons to manipulate information, you move atoms etc to produce heat. so it seems to me all kinds are really one, kinetic

I’m currently pursuing a masters in VLSI, so thanks for introducing these concepts to people! Although the built in impedances in metal and semiconductors will always overshadow the Landauer limit by several orders of magnitude. But this is an interesting thought experiment

The fact that information contains energy always boggles my mind.

Great video! I learned a bunch of this in university a million years ago but you do a super job of simplifying a really complex set of concepts. Kudos!

This is one of my favourite videos of yours. Most of them cover topics I have a fair bit of familiarity with, but your "where's the mystery?" intro made me realise I've barely thought about this at all

Great video, Jade. Thank you for introducing such a complex topic in an easy and fun way. 👍

The thought experiment I was given when learning about reversible computing referred to the elasticity of atomic bonds and how energy could be returned when a molecule returned to its original conformation.

Thank you. I had never heard about the Landauer limit even though I was a physics student. Very good explanation.

Back in College in 1984 I created a circuit gate simulator on my TI99 computer that allowed the user to place circuit gates onto the screen, connect them and then input values And then compute the output. Given enough memory, the simulator could reverse lookup the initial values. Thank you Jade for reminding me how much fun I had in college. You are an awesome person with an unlimited imagination.