You can mix 10 marbles until they sort themselves. Why not 100? 

Corrections and FAQ in this comment! 0) If you want to see the ink machine ideo about turbulent and laminar flow in a tube: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qm5AHAb0SmY.html and if you just want to watch it go, I have a 45 minute single cut: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-DtYVYfOvgKE.html 1) I'm a little loose with the definitions when I get to the interchangeability of entropy and energy, but that's because it gets really complicated in a hurry - maybe a topic for a future video. What I'm referring to is "thermodynamic free energy", which is not conserved like "real" energy. If you have a bucket of water on a ladder and you let the water pour out of it into a bathtub, you could extract energy from that process with a paddlewheel or something - that's "free energy" being spent. Once the water lands in the bathtub, the kinetic energy of it falling goes into heating the water, so now the energy of the water is in heat, and there's nowhere to put the waterwheel, so the energy, although it's still there, is kinda useless. Entropy is exchangeable with "thermodynamic free energy", not "real energy". 2) 5:05 "proobability" 3) When talking about osmosis, I intentionally swept enthalpy of mixing under the rug. there are other (real, non-entropic) forces that can increase osmotic pressure in certain cases en.wikipedia.org/wiki/Enthalpy_of_mixing 4) my “push the marbles to one side” demo may LOOK like the classic “maxwell’s demon” hypothetical, but it’s supposed to represent what’s actually happening near a REAL semi-permeable membrane. I think the ideal “demon” would not produce osmotic pressure, but even in this demo of 20 marbles, there was some measurable osmotic pressure 5)

Matt Parker would have filmed coin flip attempts until he got 10 tails in a row, then just casually throw the footage in without further comment.

The three laws of thermodynamics: 1. You can't win. 2. You can't break even. 3. You can't even quit the game.

As a Physics TA this is absolutely GOD tier Physics education. You've perfectly communicated the basics of undergrad-level Statistical mechanics and Thermodynamics and given a solid foundation for the rest of the math and equations without using ANY Jargon. Like Einstein said, if you cant teach it to a 6 year old you don't understand it well enough.

There is a consequence of entropy we deal with in our day-to-day lives at the macroscopic level: tangled wires. There are so many configurations where wires are tangled compared to the few configurations where they're neatly separated that they have a tendency to become tangled with the energy input from random jostling.

Imagine the ink in the water system shot out and the ink cloud spelled out *“Entropy, pfft”* and then dissipated- but the camera broke.

I like to use this example when someone says “well it’s possible.” For an extremely extremely unlikely event. “Yes, it is possible, it is also possible for every molecule of oxygen in the room to shift up 6 feet, but I’m not about to spend my whole life standing on chairs to avoid suffocating.”

As a biologist I'd never really looked in to why osmosis happens just knew that if different concentrations of fluids are separated by semi permeable membranes it occurs, thanks for showing me why

So you're telling me there *is* a chance?

I LOVE the overall explanation, but I have a little nitpick about the sugar/water example: At sufficiently high sugar concentrations, statistics is not the only force driving the dilution, but energy (mixing enthalpy) will be released by changing the intermolecular interactions between sugar and water (there will be "free" water instead of only "hydration shell" water touching other "hydration shell" water). By chance we actually produced a physically-chemically better, albeit less tangible, example, when decommissioning an NMR magnet a few months ago: We closed the helium pressure sensing line at the magnet cryostat, but left the pressure sensor at the other end connected. Because the line (plastic hose) was more permeable to helium than to air (as most things tend to be), the pressure inside the hose actually decreased by some 200 mbar below ambient pressure over a few weeks. Helium diffusion from the inside to the outside was more likely than the other way round due to the concentration gradient, and air diffusion in the other direction was hindered by the material of the hose. However, there are no relevant interactions between the different gases that would contribute to this, at least not at the pressures and temperatures we are talking here.

Dude is actually Maxwell's demon with balls.

I guess a non circular way of phrasing the second law is "physical distributions of things will resemble statistical distributions, and those distributions get narrow if you have enough things"

This made me think of another way of explaining why a systems entropy increases with the coinflips : If you have a random system of coins, lets say 6 head and 4 tails, and you have to randomly pick one coin to flip, you are more likely to pick a coin showing head since there are more of them, then when you flip that coin, you can either land on head and nothing changes, or land on tails and entropy increases. This makes it clear why any system tends to entropy. In your example at 9:16 you flip all the coins at once instead of picking one at random to flip which made it less clear to me why it would tend to increased entropy. Thanks for another great video :)

12:30 this is a great visualization why it's /theoretically/ possible to throw a tennisball at a brickwall and have it quantum tunnel through. But the /chance/ that every single particle of the ball dodges every single particle of the wall in it's path is less likely than the ink reversing out of it's "spike". 14:30 I was already wondering why osmosis filtering requires pressure to work. Now I know. Because without the pressure, the water would "prefer" to become dirtier instead of cleaner.

This is why production of industrial chemicals often runs at high temperatures and pressures, often in a gas phase. It's basically to beat unfavorable chemical equilibria... Sometimes heat is used just to speed things up if the product formation is thermodynamically favourable but kinetically unfavourable. The product is often continually separated from the reaction mixture to keep its concentration low which favors more production as the system continually approaches chemical equilibrium. One of the oldest of such processes is the production of quicklime in a lime kiln. Here calcium carbonate is roasted at high temperatures give off carbon dioxide, leaving behind highly reactive calcium oxide melt used for making cements. The quicklime "wants" to turn back into calcium hydroxide or carbonate once it cools down, because different conditions favor different products. This is why it's so hard to make pure chemicals, especially organics - sometimes it's super tricky to separate a single compound and this explains why 98% purity costs $10, 99.9% purity costs $100 and 99.99% purity costs $10,000+

This is so cool, I have never really considered that "entropy always increases" is not as much a physical law as just a restatement of the law of large numbers in an unbounded universe.

Here's an interesting fact: a microstate is mathematically identical to a function, and the collection of all possible microstates is the same thing as a function set. So the configuration of a system with n-many particles where each particles can be in one of m-many states is mathematically equivalent to a function f:n→m. There are exactly m^n possible functions/microstates.

Oh cool. So "Do you know why is it hard for things to be 'in order'? It's not because it's hard, it's actually because it's very improbable!"

As a high school physics teacher I am often frustrated by poor explanations or loose definitions of entropy. This is outstanding! You have explained it in a way that non-physics students can understand. This is extremely helpful for understanding biological systems, heat transfer and the universe in general.

i feel like alpha phoenix has gone from "applied science" channel to a more "steve mould" type explainer. im here for it

Thank you for explaining this! Everyone has always explained entropy to me as a definite thing not a statistical thing. They always said "Your laundry will never be perfectly folded after a trip through the dryer" when it is *possible*, but just insanely unlikely. Your explanation actually makes sense!

Perfect timing! Our undergraduate thermodynamics final exam is tomorrow, and I just shared this to channel on our student discord. Already helped a couple people remember how entropy works.

5:30 I love that you KNOW there are thermodynamicists watching...

12:10 Nice to see "10 billion human second century" as a unit :)

This is legitimately like one of the best educational RU-vid videos I’ve seen in my entire life (and I’ve seen a lot). Hats off to you for explaining so so well and so thoroughly.

By far the best video for understanding entropy from scratch that I've ever seen. I had a lot of these thought experiments bouncing around in my mind for years. Awesome to see them manifest in a video that's so well made and intuitive.

There is an infinite number of monkeys outside that wish to speak with you about a script for Hamlet that they've worked out.

Veritasium level explaining + >steve mould level demonstrating. Very well done, immediately saved to my physics playlist!

In my opinion this is the best science channel on youtube. Consistent quality, with great demonstrations and approachable explanations!

This guy is like a less evil version of Veritasium. To be clear, I'm not implying Veritasium is evil, I'm just taking a 50/50% chance this guy's less evil, and when it comes to making defamatory statements, I like those odds.

This is absolutely the best explanation and demonstration of entropy I've ever seen! Thank you! ❤

Watching you is the best thing that I have going for me in my life right now. Thanks for sharing your work!

wait. you're not styropyro

Love the discussion with the osmotic membrane. This helps explain 'reverse osmosis' desalination plants. It takes high pressure pumps to 'push' seawater against the membranes to get freshwater on the other side. Without the external source of pressure, we wouldn't get nearly as much freshwater because it 'wants' to go dissolve back into the seawater side. (edit: wrote this before the end of the video where you explain just this. I guess I jumped to this conclusion from the first part of the video)

While i learned about entropy at university, I really appretiate the effort you put into these low-level, tangable examples and models! The time you put into making sure that this concept of entropy is well explained for nearly everybody to understand is astonishing! Love your work, keep on doing great stuff!

Absolute banger, your intelligence and passion is on full display, again. Award worthy content.

Another aspect of entropy WRT to the current state of the universe which is often glossed over: Take a pebble being dropped into a body of water, for example. The reason why you never see a stone being randomly spit out of a lake is not merely due to the fact that such a thing would be "unlikely", but quite simply because gravity cannot be reversed! And it is worth mentioning, because a lot of people seem to think time reversal to be a "fairly trivial" affair. Which is of course rather irritating, considering that it is in fact not. Great video, by the way! I love these kinds of deep-dives into the world of physics.

Thank you for making such high quality awesome entertaining educational content.

Congratualitions for the great video, it's one of the best explanations on entropy I've ever seen.

The only video I've seen in the whole RU-vid that talks correctly and without unnecessary bells and whistles about entropy. Congratulations

For a split second ALL the air molecules in my room gathered in one corner and my head 🤯..

DNA is an entropy reducing device, but it requires energy to do so. Animals eat living things, so they first increase entropy before decreasing it. Plants get energy from the sun as its entropy increases via nuclear fusion.

This is the best video on entropy that I have ever seen! It was a joy to watch

love this video . im in hvac industry and this brought back the studies in entropy we did way back then .great to watch

maxwell's demon casually boiling me using a door

It may be useful to compare extreme improbably to other things that we're familiar with: getting struck by lightning 3 times the same day, earth being hit by a devastating meteor, etc. At some point, it becomes much more likely that earth will end than a fluid and ink arranging to spell your name.

your explanations and examples are extremely well done and thought through - AWESOME!!

THE single best concrete explanation of entropy I've ever seen, hands down. Thanks!

PBS Spacetime has a great episode (I think? I don't remember exactly where I heard this actually) where they posit that life is purely a consequence of the Universe's march towards higher entropy. Life's "purpose" is basically just to increase entropy if you look far enough down; all we really are is walking chemical reactions, and in the case of intelligent life it's even more true because we consume at a greater rate than life would otherwise. By this line of thinking it is essentially guaranteed that more intelligent life exists, isn't it?

shuffle sort, once quantum computers work, we can basically sort anything in one iteration, by having "unlimited" shuffles at the same time and one of them will be sorted after :D

Every time I see a new video on this channel I'm more and more convinced that I'm watching a future star in the realm of popular science. Keep giving your videos the same amount of care you're giving them here, and success will be beating down your door.

This is the best demonstration and explanation of entropy I've ever seen. Thanks!

first 🎉🎉 btw, I love your videos ❤

I don’t think this explains why and what direction time flowing. I once said a white hole(time reversed black hole) is not white, because light is coming out from eyes back to the white hole. It doesn’t even have colour. Same can apply to your idea, still nothing restricting time to go backwards.

As always, such a great video!

The best explanation of entropy I have ever seen. Thank you!!

This is the best explanation of entropy I've ever seen. There was a Steve Mould video that was also really good and explained things well, but the dive into statistics in this video really tied everything together and made things make a lot more sense to me.

I thought I had a pretty solid grasp on basic thermodynamics and entropy from university-level chemistry, but your explanation and demonstrations take it to a whole new level!

Well done, great video! One of the best I have seen on entropy, and really shows the statistical nature of it - that as the number of particles increases, the likelihood of them all separating out on their own quickly gets very close to zero. Not zero, it COULD happen, but it just never will. This just reminded me of the infinite improbability drive in Hitchhiker’s guide to the galaxy. In that book, you had the room full of monkeys at typewriters who came up with the complete works of Shakespeare. Again, great job!

Your channel is awesome. Every video is really intuitive. If only this video had come out before my thermodynamics final last week 😂

Awesome work. Thank you for the lesson. It has taken me many years to understand entropy. Excellent methodology to expose nature of entropy. Well done

I appreciated it the final connection between entropy and energy. I didn't see that crucial step in other similar videos. I'll have to watch this one again a few times until I really understand everything that's going on.

Goddamn I love your channel!! This is the best demonstration of entropy I've ever seen

Really high-quality video. Still trying to wrap my head around parts and really understand them, but it's getting there. Thanks!

Very intuitive and thought provoking explanation. Thanks for the video!

Really excellent explanation of some pretty counter-intuitive stuff. Top tier physics communication!

This is the most unique way I've ever seen entropy explained. And I love it!

This is the best video I've ever seen on entropy

Great explanation, like usual. This ties into the feasibility and promise of high entropy alloys of 5 or more equi-molar elemental constituents (affectionately called chaos alloys). With enough heat and time in the right closed environment during smelting/forging and subsequent cooling, quenching, and tempering procedures, you are almost guaranteed to be able to predict with high probability the possibility of some sort of stable metallic crystal or amorphic structure at room temperature from basic information of the target constituents off the periodic table and some surprisingly simple formulas and macroscopic intuitions. And although you'll never be able to even remotely predict the exact properties of the resulting alloy without an expensive amount of compute because of the computational irreducibility of the massive entropy, with some careful consideration you can nudge the phase space of possibilities to at least narrow a bit in on some pretty exciting exotic properties which could revolutionize entire industries practically overnight. Room temperature superconductivity and the like are obviously enticing possibilities, but I've already seen demonstrated in a paper last year a high entropy alloy that demonstrated the unique and potentially quite useful property of actually getting harder and tougher as it was heated. The possibilities for meta materials approached by the method of multiplicative equi-molar elemental formulation is quite possibly the most exciting and likely branch of science to give us a concrete technological leap in the near term future (imho).

Wow, this video is amazing. Thank you so much!

I want u as a professor, i absolutely love this kind of videos and the way u can go Deep with thinghs explaining the Essence of all

Well now I need to look up how 3-angstrom pores for RO filters are manufactured.. Amazing video as always AP. You share the pinnacle of science education on RU-vid with a very, VERY small crowd. Your effort is much appreciated!

This is probably the most clear explanation of entropy I have ever heard

this is fantastic practical work. bravo.

I like the video. You managed to find a sweet spot with not too much oversimplification. Maybe you can do a follow up on how temperature can actually be defined from the entropy and how system with a negative absolute temperature like a laser is effectively hotter than any positive temperature system. Also the entropy being a logarithm makes it additive when two systems are joined but the multiplicity of the combined system is a product of multiplicities of its parts. That makes it very clear as to why the logarithm.

I started watching this video, expecting explanations on probability alone, but was pleasantly surprised by your relations and applications to both physics and chemistry! I hand a like and sub to u sir! 😂 thanx for the quality content 👌👍

To be clear, the increase in entropy is not from mixing per se. It's from random diffusion of particles down a concentration gradient. The reason two solutes are observed to mix in a container of solvent is because they are randomly diffusing from one side of the container to the other, largely independently of one another. This process is driven by the natural (probabilistic) tendency of particles to move (diffuse) from areas of higher concentration to areas of lower concentration. The entropy increase is not because the mixing of the particles is a more likely configuration. It is because the spreading out of the particles of a given solute into the entire volume of the container is more likely than finding them all concentrated within a small region. The diffusion of particles down a concentration gradient is an example of an entropy increase, as the system transitions to a higher entropy state by occupying a larger accessible volume. But the mixing of the particles is purely incidental to the process.

Very interesting! Thank you so much, Brian! A big hug. Luca 😊

Your second example with the 10 balls was a beautiful example of entropic action and probability… loved it.

What an extremely nice and interesting video!

Absolutely awesome video!

Amazing content! Thank you.

I love this guys exccentric ADHD style enthiusism. And his mad videos. Nice geezer.

Love your work 💜 The joke with the lottery is right down my alley. 😂

Cute visuals. I love using excel too for things like this. But you gave me some inspiration on some number theory. Funny how things can tie together.

This video has increased the entropy in my brain.

My goodness what a career ahead of you

Entropy is also related to the difficulty of describing the state. All 10 are heads (or tails) is easy to describe and thus has low entropy. But naming the state of every coin is difficult to describe, so states requiring us to enumerate which are heads (or tails) has higher entropy. "Only coins 1 and 7 are tails" requires more detailed information than "None are heads." It is NOT merely human psychology involved here because entropy has been increasing MUCH longer than there were humans to be fascinated by it. Additionally, dye molecule position requires substantially more resolution than the left (or right) side of the box. Increasing the resolution in 3D is equivalent to flipping the coin more times... each 3D molecule-sized box will contain either a water molecule or a dye molecule (more precisely a dye molecule or several water molecules having the same volume). But even this requires us to 'round off' the dye molecules' positions to the nearest box. Quantum mechanics places the phase space resolution at Planck's constant, h. And this leads to the final problem with the demonstration: Position alone is not sufficient to specify the system state... momentum (or velocity) of all particles is also needed. Although the marbles were separated, they were NOT at rest nor did they have the same non-zero momentum.

The last time I felt so enthralled by a subject but also needed to rewatch the video again and again was Vsauce’s “What is down?” video. This is amazing, thank you

what a beautiful demonstration

This channel Is a gem

Great video with some clever demos!

Thank you so much for this demonstration! As ever, you really got me thinking about something I already "understood." This time just thinkin about how it's funny that we describe a perfect equillibrium as "more disordered" than an "unstable/unlikely" arrangement

How fitting that this video came out exactly while I have entropy and all things around it in school XD

Really really great video!!

just fantastic, thanks man

what a beautiful video and demonstration

Fascinating. You are amazing. Thank you@

what a super explanation. thank you very much!!

Amazing video!