The Mysterious Entropic Force
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I love this subject, I liked it when I studied it too...
When entropy decreased we called that an open system, otherwise it was closed.
Like life on earth has a decreasing entropy. That's an open system. But when we take the sun and the energy that's coming from it the system will have an increasing entropy, now the system is closed...
Always thought entropy was the natural erosion or "settling" of things
Thank you very much for this. In calculations of steam engines, entropy is fairly simple. In theory, it leaves me repeatedly perplexed.
this is all good, but can I melt steel object by placing incredibly hot tungsten ball on it?
In the specific simulation you showed at 4 minutes the particles actually attract each other which is why it springs back. So the particles are pulled to the center of mass, but one end is anchored causing all particles to migrate left.
So all I have to do is spin my room?!
You spin your room right round baby right round
@@btd5311like a record baby right round round round...
Or i rock ur world
If it's in boxes yes, or shake it really hard if its spheres. 😁
Um should i spin the world?! Wait a minute... its already spinning... Wait what
Another thing to consider
The dice and nails also reached a state where the gravitational potential energy of the system was minimized, the disordered arrangement took up more volume meaning there were lower states the dice could be in if organized.
The gravitational potential energy was thus, dissipated as sound and heat.
This is equivalent to the nature of living systems. They exist in what we would call a more ordered state, but their capacity for converting useful forms of energy to waste heat more than offsets any apparent decrease in any other aspect of entropy they cause.
Reading that made my living system fart.
@@cosmicraysshotsintothelight doing your doody
Seems work was done on the system with the twisting torque input or shaking the nail box. That kinetic energy converted to waste sound/heat means entropy increases. Gravity is another static input to the system.
I think this might be the main reason they align.
@@H0A0B123 Shimmy Shimmy Ko Ko Bop!
Does entropy also explain why elementary school students never line up in a straight line?
Did you try shaking them?
Random and chaotic.
Bro…it might.
I was really just thinking about what implications this phenomena has on living organism behavior, not just these inanimate objects that are being observed for the video
@@juroph7😂
This is a wrong explanation.
The spontaneous orderly arrangement in the example is due to the effect of gravity. Dice can lower their overall center of gravity when arranged neatly, and the same is true for nails. If gravity is removed, such as by astronauts conducting experiments in the space station, you will see that neither the dice nor the nails will spontaneously organize neatly.
In the animation the Gravity is switched off so you have a point.
@@andymouse Maybe It approximates the dark matter flowing over and through us. Galaxies start out as ring galaxies and "acquire" arms and bars and get warped along their rotational equator and things due to perturbations from other stimulus. An in space simulation would be all the dice in the cylinder in a random meander. Similar to a space containing a gas. It would take longer than it takes for tar to drip to get the data.
But if you remove the gravity of Earth or any other massive object the dice themselves would still gravitationally attract each other and they would form a clump with mostly face to face contact, very similar to the way they are arranging in the bottom of the tube.
Shaking in combination with gravity, yes.
@@aSphericalCow618 It's shaking plus gravity. Otherwise they sit as at start of video, further apart and unoriented.
I'm a physics student, and to my limited knowledge, the entropy of the dice did decrease.
But the process still happened because of the release of potential energy when a die falls.
The spontaneity may be determined by the change in the Gibbs free energy, which is given by dG = dQ - TdS (assuming isothermal and isobaric process). If dG < 0, the process is spontaneous.
This is because the increase of entropy of the surrounding (-dQ/T) compensates for the decrease of entropy of the system (dS), thus abiding by the second law of thermodynamics.
In this particular case presented in the video, since the system is not isolated (meaning, work and heat can trespass the boundary of the system), the decrease of entropy of the dice is compensated by the increase of entropy of surrounding caused by the release of heat that generated by the falling of the dice.
I genuinely enjoy every video of yours! Thanks for uploading such an amazing video :)
It seems a better explanation.
This makes intuitive sense. The demostrations in the video are wonderful to teach how crystals form: the particles slot in the position with the lowest bonding potential energy, in the same way as the dice and nails slot in the position with the lowest gravitational potential energy. Would you agree? (PS honest question: I'm a high school teacher who has to teach chemistry with a degree in botany 😅)
My understanding is that increases in entropy are increases in homogeneity. In other words, one subregion of a high-entropy region should be difficult or impossible to tell apart from an adjacent subregion with the same level of entropy. To me, that sounds like a crystal lattice. The term "order" was, IMO, originally slightly misused when the terminology for talking about entropy was getting established, since some of the physical effects of increased entropy are at odds with our natural language use of the term "order" (and its inverse, disorder) to refer to things like how tidy your room is, or how regular a printed pattern is.
@@Mikee512 the third principle of thermodynamics can be stated as "a perfect crystal at 0K has 0 entropy", which to me seems at odds with this interpretation. A perfect crystal would be perfectly homogeneous, with each region indistinguishable from any other, corresponding to a single microstate. Am I wrong? 🤔
So you're saying falling dice are hot?
I think if whoever the first person to use the word "disordered" to dscribe entropy had instead used "homogenous" or something I think we'd be like 50 years ahead with our understanding of physics and information theory
entropy was devised before we even knew there were atoms. they had some "energy available to work" thing going on.
Doesn't work either : case in point oil does not mix with water, and homogeneous emulsions separate into distinct layers.
The first use of entropy came from the observation that heat transferts spontaneously goes from hot stuff to cold stuff, and that this puts a hard limit on how efficient a thermal engine can be.
The modern understanding of entropy is that it is a measure of the number of microscopic states a system can be in based on the values of observables that can be measured at our scale.
The channel alphaphoenix made a really good video recently if you want a more in depth explanation.
"homogenous" is closer but not quite right. I think "likelihood" is a better description but still not perfect. If you allow a system to evolve undisturbed for an arbitrarily long amount of time, taking observations at random times, higher entropy states are more likely to be observed over time.
To me the best description of entropy is it’s the act of something reaching its most stable state. Like with these dice being organized like that the dice is more stable than when they are disorganized. Rust is chemically more stable than iron.
Yeah a splattering of blue and red paint has less entropy than a smooth coating of purple paint (or however the paint combines)
'Amount of free volume per dice increases'. I thought that the amount of free volume is the same before and after aligning dice in a finite system, it is just that the same 'old' free volume is now concentrated in 'new' free volume in space continuously, above the dice, not scattered between dice.
You are correct
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
Gotta disagree with the reasoning that there is more entropy in the ordered dice because they are more compact and "have more room to move around." They only have more room compared to the height of the disordered state. The dice are not actually concerned about the height of the disordered state, so I would argue that they are in fact at lower entropy since the room they care about (to the sides and below them due to gravity), is less, and there are fewer opportunities for the dice to move around.
I think this is true if you only look at the dice. But we are looking at and comparing the system in a packed state vs a random orientation state. When looking at the system as a whole we must keep the volumes the same.
Yeah.
Entropie relates to the number of microscopic states that have the same macroscopic properties.
The ordered dice have lower entropy since there are fewer such ordered states than unordered states (roughly, you can orient an ordered die in 24 ways, an unordered one in many more ways).
The fact that the system spontaneously becomes ordered does not mean that that order has higher entropy.
This is incorrect. When the dice are disordered, many of them are effectively jammed and can't move at all. On the other hand, when the dice are ordered, each dice is free to move a little bit. They don't have much room, but remember that entropy is related to the number of possible microstates. It increases with the factorial of the number of dice when they can all move.
Entropy-driven crystallization is an entire field of study. It's really counter-intuitive, but the explanation in this video is correct.
@@cwpeterson87 Dice don't have to move for entropy calculations; moreover, if they are well packed they would also not move. That is a red herring imho. I could for instance swap dice (even if they are blocked, I can still imagine two states that differ by a swap); thát gives multiple microstates with the same macrostate. Similar other processes like that.
Most compelling to me is that this is completely analogous to crystallisation, and a crystal has lower entropy than - say - the corresponding gas.
There are lots of other effects here. Like, the dice fall down, thus decrease in gravitational energy, which energy is dissipated such that the dice warm up. And thát heating still increases entropy in compensation. (They release heat, just like crystallisation does btw.)
The argument in the video that the packed dice have air above them to move to is not correct either in my view: it requires energy for dice to move up there against gravity, so that is no longer the same macrostate; it has different total energy. (And on top of that, the jumbled dice leave exactly the same room for air among each other.)
The dice aren't "concerned" with anything because they're inanimate 😂
Wait a minute...
Entropy increases in an "isolated" system, but the dice in the jar cannot be considered isolated if you apply force to shake them, right? The whole system is the jar + your hands (or your drill), am I right?
If so, are we sure that the entropy of the dice hasn't decreased if that of the whole system, including the drill, has increased?
As with your A.C. where the entropy of the fresh air has decreased but the overall entropy of the fresh + hot air has actually increased?
Or as in a living organism, a commonly accepted definition of which is a "local entropy reduction", yet implying a clear increase in the entropy of both the organism and its environment?
Right, I have a feeling the video is wrong due to the outside force and the consquences of its use being totally ignored.
*"If so, are we sure that the entropy of the dice hasn't decreased if that of the whole system, including the drill, has increased?"*
I don't understand your concern. Yes, entropy of a subsystem can increase over time. And yes, entropy of a closed system increases over time. Not only is there no conflict, but the latter necessarily implies the former: That is, regardless of how arbitrarily you partition a closed system, there must be at least one subsystem of it in which entropy increases.
in this demo, each die represents a "particle" and the shaking plays the role of "in contact with a thermal reservoir".
It's an analog for atoms with a temperature, so they would be shaking themselves like the rubber band example.
Entropy of the dice has, in fact, increased. They've lost a bunch of potential energy. The "extra volume" doesn't increase the number of potential states (that stays the same regardless), the "extra volume" instead shows that potential energy is lost, because the average elevation of the dice has gotten lower.
2:35 sounds fishy... please check:
1. microstates in the Bolzmann formula have the same energy. Here, if any dice goes to the free space above, the system will have its energy increased by the work against gravity. This breaks the condition of the microcanonical ensemble
2. Microstates are equally possible, however we don't see dices jump into the free space by their own will, therefore the shown state has much larger probability to be in and this breaks the condition of the microcanonical ensemble
I agree with your description, but bear in mind that this system wouldn't be described by a microcanonical ensemble, because it is not isolated. In fact, Boltzmann entropy would not be the correct expression for entropy in this case I reckon.
This looks more like a (N, g, T) ensemble, where available states are definitely not iso-energetic. Further thought is necessary on my part
@@andreacosta7712I guess you've meant canonical NVT ensemble. I agree with you, it should be more suitable in this case. However, I played along with the author, who decided not to introduce Gibb's formula. However even if the energy distribution of microstates was considered, my point (2) would still hold.
I actually try to lead to an idea that the author has some a sense in his words only if he never stops shaking the jar and even in this case it could be hard to say smth specific about energy distribution of states and the resulting entropy
Definitely, any kind of thermodynamical reasoning only holds if the shaking is ongoing, aka constant temperature.
What I meant was indeed NgT. Volume is not constant, but gravity is. In a way, a constant-force ensemble is equivalent to a constant-pressure one, as in NpT, which is described by Gibbs free energy.
My general point is that in this demo, the interplay of energy and entropy is what actually explains the phenomenon, so reasoning in a microcanonical framework does not give you the full picture, because entropy is constant in it. But yes, point 2) still holds.
Ah entropy, the 3rd wheel of thermodynamics
three wheel bicycle. 😂
Third wheel is what makes it a tricycle
More like a fifth wheel you know the company nobody wants around 🤣
Quite the opposite. It helps you so much to find properties of many Systems.
Ah
They all align expect for that CHAD nail at the bottom 0:57 seconds
Sigma nail behaviour
Sheeples. am I right?
Very based. "I don't conform to your laws of physics, you science bitch!" - Nail Chad.
I'm nothing like yall 😎
that was actually just a nail like object
To my understanding entropy describes particles "desire" to reduce their energy to reach the most stable state. The dice prefer the tightly packed state because here they have the lowest amount of potential energy. Also it takes a lot more energy to break that state apart, because the previous unorganized state could be broken apart by the tapping / rotating, the new state however is hardly affected by it.
Indeed. When you have packed particles, if you free them on a bigger room, they redistribute to reduce their energy. On the dice scenario, this happens also for reduce their energy.
isn't that enthalpy?
That is enthalpy. Entropy is simply disorder.
Every time I'm pretty sure I have a solid understanding of entropy, something comes along to prove me wrong! Nicely done.
I feel like I've been brainwashed
Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box.
he's wrong - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
AL is an idiot.
The trick here is not to compare the original disordered dice configuration to the final ordered one, but rather to imagine the distribution of dice orientations while the container is being shaken. At equilibrium, most of the dice align and the ones near the top are constantly and rapidly bouncing around.
If the container is not being shaken, the entropy of both configurations near zero because the dice have almost no probability of changing state. And analyzing the situation becomes harder because the disordered configuration will have a higher energy level due to potential energy than the ordered configuration
This is true but a more practical role would involve calculating the partition function. We need to incorporate positional and configurational entropy due to the limited volume. This would be more a more detailed approach and would incorporate both positional and potential energy considerations.
If we replaced the dice with smaller particles like those Einstein first observed brownian motion in, it seems clear the unpacked disorganized dice are much higher entropy. Random disturbances are much more likely to lead to an unpacked vs packed state. For every 1 packed permutation, an enormous number of translated identical ones. Am I missing something?
So the few at the top have more entropy but most are trapped in the structure and have less.
Now I don't understand entropy.
😂
Basically the smart way of saying disorder or mess
@@nonabroladze8203 no it's not mess or disorder. they are just the more probable outcomes. it just mesures the number of arrangements particles can have(it have more to do with the distribution of energy rather than particles) . a cube of ice have almost one arrangement of atoms while vapor can have an astronomical amount of arrangements. vapor got more entropy than a cube of ice it's not about disorder. disorder just tend to corelate with it in most cases.
@@nonabroladze8203 as the guy showed in the video there are more ways to arrange the dice in an "ordered" maner than there are to arrange it in a disordered manner even if the entropy is high the cube arrangement will get more ordered with time.
@azouitinesaad3856 ty
I read in a book that way and that's how I knew it😅
This is not entirely correct and in fact could be incorrect. It’s not black and white. We have to keep this simple and not try to manipulate individual concepts but instead focus on the combined perspective.
Configurational entropy and positional entropy both need to be considered and calculated. If the extent of free volume significantly affects the number of Microstates that are accessible, then it’s possible the organized dice may have more entropy due to positional freedom. If the volume is more constrained, randomly orientated dice will have more entropy. We can not make the claim that one has more than the other without proper measurement.
If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowws to reduce the volume in the ordered dice system, Then it has lower entropy.)
Excellent video, but I think you have it wrong with regard to the dice and nails. They settle when jostled into the lowest energy state - that being the lowest overall point in the gravitational field they are in. Do the same thing in a location without gravity and you'll get different results.
I agree with the rubber band example however. Note that stretching a rubber band heats up the rubber, and it cools again when it contracts. This is consistent with entropy. The nails and dice would also heat up (or increase in average speed) if you jostled them in zero gravity just like the rubber by the amount of energy expended to jostle/stretch.
Entropy is simply a measure of how likely a configuration is. Sure, it's possible that rubber band could stretch itself just sitting on my desk, but with 100's of billions of molecules in it all needing to do essentially the same thing at the same time over a long period of time (contextually speaking) a mathematician would call it a statistical impossibility.
I'm not sure about the rubber band one personnally, and if their is a contribution the force produced would be almost nothing compared to the intra and inter molecular force involved in an elastic.
@knurlgnar24 Agreed, Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box. I stopped watching after that botched intro.
Reminds me of how the initial state of the early universe would have appeared about as random/disordered as possible yet gravitationally speaking was very low entropy.
You’re living in a dream world neo.
Much ❤ Love
🌎🌏🌍☯️⚡️
World🌞Peace
but it's hot af.
The initial state of the universe is extremely ordered. All matter existing in the same point. There is only one configuration for that to be the case.
@@user-zf4dn7rz4b It wasn't a single point. The universe before the big bang was still infinitely large, it was just much, much more tightly packed. At least, according to the widely accepted theories.
In the beginning God created the heaven and the earth.
The ordered jar has less entropy, with the dice compacted there is less positions they can actually occupy while still looking the same in buik; but the total entropy of the Universe increased with the heat of the friction and collisions though. Just like life, we may seem to violate the laws of thermodynamics with all our growing and reproducing, but it's actually the opposite, we spread heat more easily than still rocks.
i noted that the gravitational potential was reduced, as all the dice are now sitting lower in the container. we need to send ActionLab to the international space station to repeat the experiment in microgravity.
The story of the dice themselves decreased, but the entropy inside the jar as a whole increased as a result by compacting the volume. Honestly though, he is using semantics.
That's incorrect, energy neither increases or decrease, the universe is moving towards the most statistically likely configuration which is the true definition of entropy.
*The 3 levels of entropy from less correct to more correct*
1: A system moving in the direction of a more disorderly state
2: A system moving towards a state of equilibrium
3: Energy and matter displaying the most statistically likely configurations
*Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
@@notaffiliatedwith7363It's not about geometry and order, it's about the most likely configuration in a given system with it's laws of physics at work
@@markmuller7962 Yep, "order" and "disorder" are subjective, so they do not always match with the entropy. A good example is oil and water separating over time when with most other liquids we see the opposite.
All those squares make a circle ... all those squares make a circle ... all those squares make a circle. ..
Every tweaker spontaneously reached for the dice and knocked their screen to the ground.
He's succeeded in circling the squares!
I also enjoy Dragonball z abridged
Hey! I like your video, but I have to ask for clarity. You treated the bowl of dice as a closed system while exerting outside forces. I believe you when you say the total entropy of the final system (inside the bowl only) increased, and the entropy of the drill also increased. Why was the outside force ignored? In another system where outside forces are ignored you may have decreases in entropy. But missing the outside force leaves the question open, does the entropy decrease in the bowl balanced by the entropy increase in the drill? Of course you explained that when looking at possible states it is favorable to pack. Further, thanks for the video, we fail to remember that "ordered" is a human imposed concept, if we define it as the low entropy states, then the bowl of none packed dice is more ordered than the packed one. But our brains like to call the packed state as more ordered.
As an aside, regarding "ordered" being a human imposed concept, I tend to think of "order" vs. disorder being recognizable patterns vs. a lack of recognizable patterns. Of course taking macro and micro into account, there are patterns that we don't always immediately recognize as such. You can quickly get into "does a tree falling in the woods make a sound if there's no one there to hear it" territory (we know the answer to that of course). Referring to whether patterns/order requires observation to be considered patterns/order vs. random chaos. The science of the impact or lack thereof of observastion of phenomena in the universe continues to be intriguing topic.
*The 3 levels of entropy from less correct to more correct*
1: A system moving in the direction of a more disorderly state
2: A system moving towards a state of equilibrium
3: Energy and matter displaying the most statistically likely configurations
*Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
(3) need a tweak: the whole point is that all microscopic configurations are equally statistically likely (at the same energy), but there are just so many more with the "right" macroscopic variables that it always looks right.
e.g., the configuration of N2 and O2 molecules in the room (all your rooms) right now has the same likelyhood as the one with all O2 on the left side and all N2 on the right side, but there is only one state that looks like the latter, and more than Avagadro's number to the sixth factorial that look like the former, and (N_A^6)! >>>>>>>>>>>>>>> 1.
The "arrow of time" is not necessarily a more correct part of your difinition. An interesting idea, but not demonstrable. Sean Carroll (the physicist who proposed this) is a *theoretical* physicist and his idea arguably enters into an unprovable area.
@@PsymonHawkeye Actually the arrow of time is a side addition to the third concept just to make it clearer. And btw it's not a matter of hypothesis, the main role of entropy in the arrow of time is a theoretical physics *fact* aka scientific theory which doesn't have anything to do with the English popular use of "theory". It's a scientific theory, learn how science works
@@DrDeuteron Yes everything is emergence but the definition was getting too long already for a YT comment
@@markmuller7962 agreed. Idk, that was my favorite part of statistical mechanics.
I use it to disused lottery players:
Me: “ you should pick 1,2,3,4,5,6”
Them: “why? That will never come up!”
Me: “exactly.”
Good content, great in getting people to think! I have an additional way to think about this that may be complementary that I thought I'd share.
The reason a more "ordered" arrangement seems to emerge is because there are e.g. air molecules in the system which become more disordered (as mentioned with the 2nd law of thermodynamics). A good explanation where we see a seemingly more ordered arrangement is in biochemistry. Look up how protein folding occurs due to the hydrophobic effect; to me this explains an entropy-driven system fairly well. We need to remember that the system contains the medium (e.g. air or a solvent); this is demonstrated well by the visual of the closed container ending up with more "free space".
Edit: I should also mention that in the dice example, movement causes the potential energy to decrease since the mass of the dice is lower to the ground. However, since the point of the video was a model to help understand entropic effects, it's still a decent enough analogy.
Now try the same experiment without gravity pulling all items into the same direction.
"When enough chaotic and random events happens. Eventually, it leads to very predictable events."
Thats quite philosophical. So after enough observations, everything will be understood.
We are imperfect to understand all. Only God knows.
Yet the definition of chaotic and random preclude the possibility of predicting. So are the events truly chaotic or random? If they are predictable then they can't be.
@@PhokenKuul No, not if you are part of the system being analyzed yourself eg human nature.
@@PhokenKuul Made me realize that i find it philosophical because of how paradoxical it is.
@@PhokenKuulthis is incorrect. There is nothing in the definitions of chaotic or random that preclude prediction. Dice rolls are random but I can accurately predict that each number will appear 1/6th of the time in a large number of rolls.
Well, this was absolutely fascinating.
I watch tour channel mainly for how you make science topics fun and engaging with clever and novel experiments, but then every so often you deliver powerful insights expressed really intuitively and clearly. Thank you. Excellent work.
Greetings from Slovakia
Which scientific articles or books were used in the video?
He made it the F--- UP!
I finally get the description of Entropy in a clear short way. Thank you 👍🏻
This fits perfectly into my own model of (special and general) objectivity - A specially cosmos (the energetic exception) is some pattern within a higher-order general cosmos (which relative to the special cosmos manifests as chaos), i.e., the general relative array of objectivity (the energetic average). Randomness (or uncertainty) is here not "entropy/chaos" itself, but rather the maximally indecisive superposition of "everything everywhere all at once, all at different positions along the "cosmochaotic axis" such that it can't seem to decide whether to be entropic (chaotic) or negentropic (cosmic) - so it just averages out in the exact middle of the fractal spectrum.
Your videos make every hard concept seem so fun and easy
Good Morning!😃
A new day to love
I saw your journey on the Alan Pan video recently, and watched some of your content after. you should do more CZcams videos
This is of the most interesting take on Entropy I have ever seen. Very nice explanation!
Free volume is not created. The many random small amounts of volume have been combined into one larger volume but no extra has been added.
THIS.
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
My thermodynamics professor had something he repeated constantly, "now we just count the states." Right, "just". The text (which he wrote and distributed free) had an explanation of how we knew all the states had been counted. Entropy was simple, the more states possible the higher the entropy and the more probable that the system would be in one of those states. Amazingly most of the laws of gases, liquids and even solids could be reduced from this "simple" counting of states.
I'm not going to attempt counting the states of dice in random vs. ordered configurations but I'm pretty sure that from this perspective there are more states of randomly ordered dice.
My lesson I learned is that the properties which apply to atomic level particles are not necessarily those that apply to macro sized objects.
Except with the disordered dice the volume is largely inaccessible because each open volume is less than the size of a die.
@@JK_Vermont Not the issue. The video was claiming that volume was created. Not that usable volume was created or more useful volume was created. Details matter. "It's physics for Godsakes".
Big fan sir ❤
My understanding is that the jar with the dice packs in an ordered way because that decreases the total gravitational potential energy of the dice, which makes that state more likely. If jar were in a state of weightlessness, the disorganised state would be more likely.
Great topic! I always learn something, realize how little I know about something and not understand something altogether in every episode, it’s awesome. Keep up the great work!
So a glass full of ice cubes has statistically higher entropy than that of a glass filled with water?
Dry ice
Nope.
Snow. for that... then the macro... fractured glaciers.
No. This is one of the problems with using macroscale metaphors to describe entropy. When describing the entropy of a system you have to be consistent in what particles you are talking about. Is it the ice cubes or the water molecules? It can't be both. In your example the water molecules are locked in a crystal structure in the ice cubes but free to move in the liquid, so they have significantly more entropy as a liquid.
School: 40 min
Action lab: 7 min
But don't forget how long it must have taken him to make this video. Its like comparing eating a raw carrot to a well seasoned and cooked one. Eaiting the cooked is both easier and more efficient but the process to make it takes more time than just eating it raw.
@@grzes848909 True, but teachers have prep time too. They don't just decide to randomly throw together a lesson plan, they figure out how they want to teach a subject, just like these videos.
one is about entertainment and showing you a topic, the other is about properly going through that topic in a way that makes you understand the depths enough to work with it
Now do the homework with that 7 minute lecture...
really cool video, and love how you just casually throw in chat GPT in like "if I ask it the answer WILL be wrong", 10/10 chefs kiss
Thanks a ton! I've always had trouble relating entropy to disorder. It just never ultimately connected! But assigning it to the number of possible locations to move to/ be in makes so much more sense! Finally an explanation that lacks the internal contradictions of just being a subjective level of disorder.
4:07 you say there's no forces acting on the particles making them coil together but actually in the simulator you used the electromagnetic force is simulated, which is what's pulling them together
For me, this is the best scientific content
This really changed my understand of entropy and appreciate the perspective that life is an emergent property of a system that has evolved to increase entropy while efficiently dissipating energy. The variety of life on Earth shows that a relatively small number of different chemical elements can assume quite a variety of arrangements. Carbon is entropy's strongest proponent in that realm.
I think I need to watch this a few more times for it to sink in. Awesome explanation.
The fact that the die are packed tighter together gives each dice less options. The definition of entropy is lack of order. You put them in order.
That's not the definition of entropy. Entropy is a statistical count of the number of microstates a given macrostate system can possibly be in. It's commonly associated with what we perceive as order but not exclusively so. Eg the whole universe at the Big Bang was in a state of relatively low entropy, yet it seems to us that order in the universe has only increased even as the entropy of the universe also increases. "Order" as perceived by us isn't real, it's something our brains conditioned by evolution hallucinate.
You specifically only looked at half the definition. The full quote is:
PHYSICS
"a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system."
So yes, while the system is more ordered, the set up for the more evenly stacked dice/nails is the the shape it settles into when enacted upon by the mechanical forces. Making the eventual state it ends up in is more entropic than the original state.
It's confusing because we are taught entropy as something that happens in an infinite area, usually with gas. In a high energetic state gas moves to areas of less density. With solid objects though they tend to eventually settle together. That is how planets came to be when the universe was formed while still very much under entropic forces.
@@surprisinglyblank2392 Yes, this is the definition of entropy I learnt. The amount of energy unavailable to do useful work. If something is unavailable, it can't do anythin, let alone create a force. The fact that he had to do work on the dice and nails to align them was not taken into account.
Who else clicked on the video without knowing what entropy is..
String theory my asshairs together
Isn't that what most of his videos?
Well if you try to use entropy to clean your dishes it will take longer than your life time ...
How many monkeys does it take
@@cheeserdane if I used entropy? The word n meaning or the real whatever that does and doesn't exist
Beautiful video, nicely put, I want more videos about entropy from you!🙏
I've quite recently finished writing my PhD thesis on entropic phase transitions in some specific systems. I have a whole section of a chapter devoted to "trading" one type of entropy for another type for a net entropic gain. I find this phenomenon very fascinating and almost each one of my scientific papers has a short, "intuitive" discussion how it is applied to the case on hand.
No I’m not first
4th
0 views in 34secs bro fell off
still using this repetitive meme are we
Do one. You're as useless as first commenters.
Yeah
this comment is getting really old
It's cause 300 people had to look up entropy to even understand the premise.
The entropy gets even higher when you also start shaking perpendicular to the rotational shaking. It never gets ordered.
I always know I'll love videos from you! ❤❤
We can count on you to always come up with something so interesting it mesmerizes.
I’m pretty sure the example of the rubber band stops being only entropic force the moment the band has to be stretched rather than just loosely in a line.
very intuitive way of showing this! great video
I love how your simple questions and demonstrations arouse the curiosity of so many. I never considered the entropy of a cup of dice before, for example.
I think the way that communicates best how I understood entropy is "The inverse deviation from an object's state at the end of time," meaning, the more entropy increases, the more closely an object will reflect the state it would be in as time approaches infinity, and that entropy is used as a way to gauge how far away an object is in an initial state from the state it will reach at the end of time
That "ow" was expected but it still threw me off guard
This is concerning for my health. I've recently had surgery and those things rendered me unconscious as soon as I got into the emergency room.
It even happens with your morning cereal flakes - it says on the box "Contents may settle during transit" But every cornflake is similar but totally different, and they will only get to a certain level of entropy! Another awesome video thank you for sharing!
What was said in the beginning of the video, that the 'ordered' systems (dice or spheres) have more entropy than the disordered ones is not correct (if we look at the isolated entropy of the packing of dices and spheres). You might consider correcting this.
These systems do not reach a state of maximum entropy, but the minimum of an energy potential (like the Gibbs potential in thermodynamics). For the dices and the spheres this potential contains a gravitational energy term, which is the +m*g*h, where m is the total mass of the dices or spheres, g the gravitational constant and h the height of the center of mass of all the objects in question. The second term is an entropic one -c*S (c is some constant depending on the thermal energy or the shaking intensity in this case). The system now tends to adopt a configuration of minimum m*g*h-c*S. The close packing reduces h and this term dominates and therefore the dices or spheres adopt a packing where h is smallest possible even if S is not at its maximum. Here minimal h and maximum S can not be reached simultaneously.
To understand this consider there is no gravity (i.e. g=0) then only the entropic term -c*S is left in the potential and the system will adopt the state of maximum entropy (i.e. all dices and sphere floating randomly in the cylinder) at the mildest shaking (i.e. c is not zero). The second case is strong continued shaking. In this case c will be very large and m*g*h will become negligible (basically g can be assumed to be 0). Then again the dices and spheres will ‘float’ randomly in the cylinder due to the shaking.
If he said 'maximum entropy' then he's wrong on that as you say. He's also mixed up on another count i'd say: If we follow the guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
This was very informative, thanks for the video. It would be really cool to see more everyday examples of entropic forces
I recall reading that this is why cables in a box tend to get tangled with each other (or headphones in your pocket).
Part of the misconception is due to the definition of entropy. The Oxford dictionary has two definitions. One is in relation to thermodynamics, the other is...
lack of order or predictability. Although your initial dice state lacked order, it was completely predictable. It will gain order when agitated in a certain axis. The second state now has order, but is harder to predict. Who knows what it will do when agitated?
Your vids and explanations have really improved lately! Keep goin good sir
This video is deeper than usual. Unexpected, but I like it.
The best explanation of entropy on the internet
I prefer to think of entropy as pointing in the direction of the arrow of time - jiggling and jostling over time will tend to produce the most common configurations. This only holds if all configurations are equally available and aren't sticky. Natural filters in life put a non-random bias against this jostling, from your example here to the gravity wells of stars and the motion of beaches, or Life's Ratchet in the cellular machinery. If once a random state occurs that locks in a position (like your orderly dice that can no longer move) then they will tend to order up even if order up states are less common, because they stick. No matter how slow the decay is or how uncommon the state of a random decay is, Schrodinger's cat will die when it happens and will stay dead (cat will randomly die but not randomly resurrect), so over long time you are much more likely to find a dead cat than a live one. Entropy was meant to describe states that are fully free to interact in the system, not natural filters. It doesn't break physics, it just doesn't fit that model.
If you think of entropy not as of particle concentration or arrangement, but as the most likely outcomes over long times scale including non-random natural filters, then a compact star or beautifully orderly beach sand are actually low entropy as the dead end of the jostling options. This kind of one-way-ness also applies in other realms like gambling - where no matter how much you win you still can still risk all and lose all, but once you are broke you cannot un-lose. The house always wins even if you have slightly favorable odds, because even a less common disaster cannot be recovered while all cumulative success is just one bad roll from being wiped away.
Entropy has nothing to do with disorder unlike described by statistical mechanics, it is related to heat.
I came out of this video feeling like I have a better understanding of entropy than ever before. Well done!
Careful, I think this is one of this channel's rare erroneous videos
@5th_decile Yeah he is wrong and Killmajaro's understanding just got worse
I run a Precious Plastic recycling workspace, here in Italy, in my spare time.
Usually I wash the plastic I collect in my washing machine (the european kind of, horizontal shaft), in a pillowcase, when doing laundry.
Often I have some boxes with sliding covers, the ones that contain carbide lathe inserts, or telescopic boxes for drills, and so on.
Sometimes I also have to wash bottle caps with child safety bottle caps (something from vaping fluids from friends and colleagues), made in two parts.
I break the external part to separate them, and then put them in the pillowcase.
Practically every time all of the parts come out from the washing machine re-assembled.
It's amazing.
I love this video you explained so much
The ideas of self organizing systems and entropy seem totally at odds until you bring up these cool examples
I took physics at McGill university with Adv Stat Mech I and II and never heard of a better explanation. Another amazing video!
Love that you need to toot your own horn as if anyone cares that you went to school. There are Christians with PhDs. Your degree means nothing.
I'm just going to consider that the jar with the dice lined up is more disorganized than the jar with the dice taking up more volume.
Very good explanation, lots of anecdotal examples.
This is why science is so great. Its about studying whats actually going on regardless of preconceived ideas or beliefs. Properties of the Universe can get confusing (especially when there are multiple things going on and many variables). Science is studying each one, recording data, repeating, recording, etc.
Humans love to see one event and assume they know everything from it...we know thats not the best way yet here we are in 2024 with 10s of millions who would rather believe what they want to more than what is real.
In thermodynamics, we were taught that entropy is the amount of energy that is not available to do useful work. As such then, something that is not available cannot create a force. External work was done on the dice and nails to get them into the ordered pattern. They did not get that way by themselves.
You can still call entropy disorder, but just be careful of what you define as your system. For example, the dice ordering and leaving the volume has higher entropy, but if you were to consider the system as only the dices, and therefore don't consider that bit of volume that "creates" later, the entropy is lower.
On a microscopic level it's easy to call entropy disorder, but on a macroscopic level defining systems is hard
The example of the elastic band and the curled string of particles was really cool!
Love the video thank you! And your book is fantastic!!
Marvellous! Best explanation I have ever seen. I almost get it now.
Nice T - shirt 👍❤️
Always wondered how science could explain why this happen.
You're forgetting the most important part of the equation, you. Conscious intervention. You interfered. You added order to a disordered system. You put it back together. You pulled the rubber band. If you haven't looked into Emergence Theory, you should.
Just stop. Go home.
There are a couple things that don't make sense to me about this. And these aren't rhetorical questions, I absolutely believe your account of how it works since you know much more about it than I do. These are points of genuine and self-acknowledged confusion.
1) If entropy depends on number of possible configurations, shouldn't the dice still have higher entropy when more disordered? You say they have higher entropy when tightly packed because there's more free volume above them, but it seems to me the number of possible configurations of the dice is higher the more volume the dice _do_ occupy, not the more volume they _don't_ occupy. I realize the dice are actually separate objects, but if we think of the volume they occupy as this connected, amorphous cloud, then shouldn't there be more possible places we could find any given die in the larger _that cloud_ is, _not_ the larger the _air above it_ is? I guess what I'm getting at is, if we consider only the configurations where the dice are tightly packed, it seems to me the probability of finding any dice in the unoccupied volume above the dice, that volume you described as "free," is by definition _zero._
2) Also, generally, how valid is it, really, to discuss entropy as a number of _possible_ configurations of a system which has a _known fixed_ configuration if closely observed? If die A _is_ at position P, and die B _is_ at position Q, then the probability of finding die A at position Q or die B at position P is zero. I know I just got through saying we can think of the occupied volume of the dice as this connected, amorphous cloud, but can we really? Isn't that occupied volume actually a precise crystal structure in the exact shape of a whole bunch of cubes, with pockets between them excluded from the manifold? By that logic, it seems to me that _everything_ has zero entropy at all times. I realize this notion of exact knowability doesn't hold at a quantum scale, where the uncertainty principles take effect, but we aren't _at_ that scale.
This is why I love Thermodynamics. This is not only about "X" particles or things moving and doing things, it's something more fundamental.
If the organised dice are basically identical it doesn't matter which position they take, it's essentially the same state, so low entropy.
If they are disorganised it does matter which position they occupy resulting in more states = more entropy.
It shows because you needed to put in energy by shaking/twisting to organise them.
Ehy, I haven't checked the entropy calculations for the dice problem, but I have the feeling that the problem can be formalized in a way to define a free energy (akin to Gibbs free energy for chemical systems at conatan p and Helmoltz free energy at constant V) for the system as a combination of entropic effects and energetic effects. The energy in this case is given by the gravitational field and the constraints of the jar. If you had the same jar (with a lid, to make things simpler) in space, the average equilibrium state would be the one with the disordered dice scattered all over the place. I think that the only reason why you reach the ordered configuration with your shaking process is because that configuration corresponds to the local minimum of free energy for the system in the gravitational field. The shaking is just a way to go from local minimum to local minimum until you have reached the global minimum.
The fact that the equilibrium of systems subject to forces is not the maximum of entropy is a well known fact in chemical thermodynamics. In fact, almost always, maximizing the entropy doesn't give you the chemical equilibrium of a system. Otherwise you could not explain things like the formation fo crystals or even molecules at all.
The second principle of TD tells you that entropy is a thermodynamic potential only strictly for isolated systems: for all other systems, you need to find a suitable TD potential to minimize or maximize given the constraints of the system. The only thing that TD (specifically, non equilibrium TD) tells you about entropy is that any irreversible process comes with a positive entropy PRODUCTION (not entropy): but for any non-isolated system, you can always let entropy in and out of the system by suitable fluxes of heat or mass.
Finally, I am sure you are familiar with the fact that since Boltzmann's pioneering work on the statistical interpretation of entropy, there have been several different definitions of "entropy" related to microstates of the system, more or less coherent with each other and the classic definition of entropy proposed by Clausius. Even without entering the rat's nest of which statistical definition of entropy you are referring to, I would honestly be surprised if you cannot find a coherent formalism in terms of free energy to describe the entropy of the dice so that it indeed decreases as it approaches final metastable configuration, thus attributing the driving force to an energetic factor.
I gravitate towards your answer as the best one. 👍
This is one of those videos that flips your brain upside-down.
This blew my mind. Thanks a lot.
Entropy? :D
This is more about a constant field of gravity acting on the contents locking them in place, and the constant work input by agitation that allows each die/bead to move out of its current local minima and fall into its new place. Once slotted into positions, gravity and force from their neighbors restrict them from moving out of place. This effectively locks them in place. It just so happens that the most 'restrictive' spaces are also the most space-efficient structures (highest packing efficiency), and crystalline structures are quite space-efficient.
Hence spheres forming a face-centered cubic instead of body-centered cubic or other patterns.
Given the magnitude of forces at play, they drown out any entropy changes you see in the system.
Try doing this test without agitation and gravity messing with the system. Try suspending them in solution of similar density. If you let the solution evaporate or drain slowly, it might shed a decent light on crystal formation too. (drain too fast and they will look more disordered, and 'crumbly' too) :D
This video reminds me of my younger days back in the 90s. I used to prepare for raves by visiting a stimulating trader I knew.
I was still young and naive and didn't understand why this friend would always take out a large bowl filled with dice and marbles. He explained that sometimes its not enough to hide the screwdriver.
As my experience grew and I met different people I understood, Dude was just protecting his electronics with that bowl.
You are a star! I am now more educated than before. Thank you!😊
this was really good, thank you
While the entropic force is a major factor in a rubber band's retraction, it's not the sole force at play. There are also:
Enthalpic Forces: These arise from changes in the internal energy of the rubber band when stretched. Stretching stores energy in the polymer bonds, and releasing the band allows this energy to dissipate.
Cross-linking: The polymer chains in rubber are often cross-linked, creating a network that resists deformation. This contributes to the overall restoring force.
The Dominant Force:
In most everyday situations, the entropic force is the dominant factor in a rubber band's behavior. This is why heating a rubber band (increasing entropy) causes it to contract, and cooling it (decreasing entropy) makes it stretchier.
Important Note: The balance between entropic and enthalpic forces can change under extreme conditions (e.g., very high or low temperatures) or with different types of rubber.
In summary: The entropic force is a significant factor in a rubber band's tendency to return to its relaxed state, but it's not the only force involved. Enthalpic forces and cross-linking also play a role, although their contribution is usually smaller in typical scenarios.
It still seems weird to call it a "force", but that's a great explanation of the increased entropy of "free space".
Also kudos for taking that rubber band snap to advance science education: I thank you for your service and sacrifice. 😊