What causes entropy?

[Dancing David]

ok, lets understand what entropy actually is. it is not a statistic, it is a state of matter. it is not a chance probability either. we are also not talking about the effects of different energies or motions on the outcome.

we are not looking for the chances that something will equilibrate, nor are we looking for it's most likely region of occurrence or a trend line or some average of a bunch of events equilibrating. entropy is not always, and does not have to be chaos theory or anything other than what it describes.

Now that is just goofy, who brought up chaos theory?

Entropy is a state of matter, now there is a great defintion. Um , sure and could you describe thats tate. It has to do with a lot of things.

You really don't understand the words statitics or probability, do you?

What on earth could the probability of radioactive decay have to do with entropy?

 

[Dancing David]

Hence the word "locally", for isn't that what a life form essentially does?

No, how do you think metabolism works and why do many life forms generate heat?

 

[Dancing David]

That particular statement? Just one.

One with lots of consequences, though.

Take your batter example, for instance. The ball is approaching, and you think you know how fast and what it will do. You swing and hit it.

However, quantum uncertainty says you cannot exactly know the momentum (mass times velocity) of the ball (or your bat, BTW) unless you give up knowing something about it's position. The very photons which are reflecting off it are changing its momentum, while giving your eagle eye an exact position. Granted this is not very important on the diamond, but it illustrates that at a very fine, very basic level of the universe all interactions are statistical; what we see at our living level looks like good solid examples of classical mechanics, but they are actually only very tight probabilities. If you deign to investigate the very small, then it will become apparent that statistics rules all.

Perhaps that's not important to you, but you ignore its existence at the cost of loosing understanding. Sort of an uncertainty principle in itself.

Um, no. A bat and ball are macroscopic, so how does the involve the HIP?
delta x product delta p > h-bar/2

Hbar is a very small number, the HIP is not distinguishable in the macroscale.

 

[sol invictus]

Can someone explain how energy and entropy and this whole probability idea are related?

Like, does higher entropy mean lower energy, etc? Are they both two sides of the same coin (no relation to the example in question) ?

The relation between energy and entropy is not as simple as that. Generally higher energy means higher entropy, not lower - because at higher energy usually more states are accessible to the system - but there are important exceptions.

Perhaps the easiest way to see that they cannot be tied together in any very simple way is to recall the example I gave above. In that model there is no energy, or we can regard all states as having equal energy, but the entropy can change (for example it can go from zero to maximum if we start with all the coins in one container).

 

[sol invictus]

Ok let me word this in the way I would think about it and you tell me if it sounds good or you disagree.

If we view a system as a sequence of discrete states, you are saying that all of the fundamental laws of physics -- which are the state transition function -- operate the same way in both directions -- which implies that the state transition function is invertible ?

Yes.

So if that is the case, the only way to determine which direction the sequence should proceed in is to look at the probability a given state would take a forward or backwards transition ? And that this boils down to proceeding along the sequence of transitions that increases entropy, because probability tells us that this sequence is simply the most probable?

If at some moment the state has an entropy that is significantly less than the maximum possible value, the probable evolution into the future is that the entropy will increase, thereby providing a time-asymmetry until such time as the entropy reaches its maximum (i.e. the system equilibrates).

Oddly, the above paragraph is just as true if you replace "future" with "past"... nevertheless, this says that the return to equilibrium (in whatever direction) is the interesting time to be alive.

 

[sol invictus]

BJ Penn jumps out of pool and lands on edge.

Impressive I suppose, but I could still tell the movie wasn't being played backwards .

What did you mean by "future appears different than the past?" Creation of the universe? Viewing start from millions of light years away (and thus occuring millions of years ago).

In the past, you were younger. The universe was hotter and denser.

Time flows in one direction. Milk doesn't unmix from coffee, fireballs don't contract and assemble themselves into bombs, smoke and heat and light don't form into a candle and wick.

The future is different from the past, or at least so it seems to us. It's very strange.

 

[shadron]

Um, no. A bat and ball are macroscopic, so how does the involve the HIP?
delta x product delta p > h-bar/2

Hbar is a very small number, the HIP is not distinguishable in the macroscale.

Oh, all right. If you say so. Jees. : pout:

 

[Dancing David]

Oh, all right. If you say so. Jees. : pout:

If you play baseball with elementary particles then it is hard to tell who is out and who is safe.

 

[Hellbound]

If you play baseball with elementary particles then it is hard to tell who is out and who is safe.

Just to offer a bit of defense, I read it as him getting to that point (that quantum effects aren't distinguishable at the macro scale). However, the interesting questions (to me) is: why? If all the particles that make up a baseball and bat are individually affected by uncertainty principles (of various forms), why don't we see them at large scales?

And the answer, of course, is the stastical probabilities. It is theoretically possible that the baseball will quantum tunnel through your bat. The chances of this occurring, however, are so low (due to the improbability of every one of millions of particles having exactly the correct quatum state to perform this feat in concert), that we'd have to wait the lifetimes of several universes to see it.

In other words, macro-scale classicality is simply the aggregate of an enormous amount of micro-scale prababilities.

 

[rocketdodger]

The relation between energy and entropy is not as simple as that. Generally higher energy means higher entropy, not lower - because at higher energy usually more states are accessible to the system - but there are important exceptions.

Perhaps the easiest way to see that they cannot be tied together in any very simple way is to recall the example I gave above. In that model there is no energy, or we can regard all states as having equal energy, but the entropy can change (for example it can go from zero to maximum if we start with all the coins in one container).

Well let me ask you another question instead, then: Is there a way to frame the concept of energy using probabalistic terminology, like we did with entropy?

 

[DarthFishy]

Yes.

Here's a simple example (this is called the "Ehrenfest urn model"). Consider two containers and N coins, labelled 1 through N. N is a large number. Every instant you randomly pick a number between 1 and N, and move the corresponding coin from whichever container it's currently in to the other. The quantity of interest is the number of coins in each container, or more conveniently, the fraction f of the coins that are in container A at any given time (i.e. f={number of coins in A}/N).

What will happen to f as a function of time? It's probably clear that f has an equilibrium value, namely 1/2 (if that's not clear, I can explain). It may also be clear that any state where f differs significantly from 1/2 will not last long (i.e. not much longer than N instants), and that once f gets near 1/2. it will experience only small fluctuations around it. All of those statements are true if N is large (bear in mind that this is a simple model for a physical system where N is often of order 10²³ or larger).

What does this have to do with entropy? Entropy is simply (the log of) the number of states that share some macroscopic property, like a value of f. For example, suppose N is even. Then there are N choose N/2 (that's a very large number) states with f=1/2. But there are only N states with f=1/N, and only 1 with f=0. That means that with very high probability, low entropy states (like f=1/N) will evolve into high entropy states (like f=1/2 or near it) rather than lower entropy states (f=0), simply because there are many more high entropy states (by definition).

What makes this a useful concept is that when N is very large, the number of states near f=1/2 is vastly, mind-bogglingly larger than the number of states near f=0. Therefore the chance of the entropy decreasing is absurdly small, so small it may never have happened in the history of the universe. As a result, the 2nd law of thermodynamics is called a "law", even though it is in fact "merely" probabilistic.

This is the reason drops of ink dissolve in water and never re-form, it's why you never see people leaping up out of swimming pools and landing on the diving board above an undisturbed water surface, it's the essence of life, and it explains why time has a direction. It's one of the simplest, most beautiful, and most profound ideas in physics.

Thanx for the great explanation and Nominated

 

[Java Man]

what is a statistical measure anyway?

An example of statistical measure in layman's terms:

Good statistical measurements. Very precise design, very expensive.

Poor statistical measurements. Not very precise design, very cheap.

Not learning a tid bit about statistics can be very expensive on your wallet. Specially when you pay for mechanical precision you're never delivered.

 

[ServiceSoon]

...Milk doesn't unmix from coffee, fireballs don't contract and assemble themselves into bombs, smoke and heat and light don't form into a candle and wick...

Screw milk and fireball analogies; based on our current understanding nature not only created itself, but it created us too. That's a feat we have yet to duplicate.

 

[drkitten]

Well let me ask you another question instead, then: Is there a way to frame the concept of energy using probabalistic terminology, like we did with entropy?

Sure. Energy is a function of the distribution of states; see the Bohr model of the hydrogen atom for an example.

It's just very difficult to work with systems larger than a single hydrogen atom, which is one reason that energy is usually treated as a primitive.

 

[sol invictus]

Well let me ask you another question instead, then: Is there a way to frame the concept of energy using probabalistic terminology, like we did with entropy?

A system has a set of possible energies. Because of quantum mechanics this set is typically discrete (with some exceptions like systems with infinite volume). Also because of quantum mechanics the system can be in a superposition or probabilistic mixture (those are two distinct possibilities, by the way) of those states; that is, it might not have a definite energy.

Generally (again with important exceptions) there is only one state with a specific energy. That means that if the system has a definite energy, it also has entropy that's log(1)=0. But since we rarely know the energy exactly and the energy levels may be extremely closely spaced, one typically "coarse grains" and defines the entropy as the log of the number of states within some range of energy, or with energy below some value, or by the energy of a canonical thermal ensemble (which is a distribution over energy states).

 

[SonOfLaertes]

No, how do you think metabolism works and why do many life forms generate heat?

I'm not sure we are on the same page here. My original post was a reply stating that life on earth is possible because of a net increase in the entropy of another system, our sun. I then marveled with another poster about the prodigious output and energy potential of our sun.

Apparently, I don't have the layman's understanding of entropy that I thought I had.

Doesn't the biosphere on earth temporarily halt the local (on earth) increase of entropy by binding, storing, and working with the energy supplied by the sun to create increasingly complex, ordered systems? If not, could you give a quick explanation of where my confusion begins? I promise to take your answer and do further reading.

Forests, for example, store the suns energy and, left unchecked, multiply (locally decrease entropy) until they reach an equilibrium state where the net entropy of that system neither increases or decreases (roughly). Of course, this only happens because of the increasing entropy of a star.

If you will say that order and complexity are not useful definitions of entropy, then I understand, and will take the various sources which partially define it that way as out-dated. Can you give a down and dirty explanation as to why I shouldn't interpret entropy in this way?

 

[SonOfLaertes]

As I slowly composed my preceding post in short breaks while at work, I see that a number of posts have delved into the matter at more depth. So forget about answering my screed above, I'll digest the efforts above and try to answer my question myself.

 

[rocketdodger]

Sure. Energy is a function of the distribution of states; see the Bohr model of the hydrogen atom for an example.

It's just very difficult to work with systems larger than a single hydrogen atom, which is one reason that energy is usually treated as a primitive.

A system has a set of possible energies. Because of quantum mechanics this set is typically discrete (with some exceptions like systems with infinite volume). Also because of quantum mechanics the system can be in a superposition or probabilistic mixture (those are two distinct possibilities, by the way) of those states; that is, it might not have a definite energy.

Generally (again with important exceptions) there is only one state with a specific energy. That means that if the system has a definite energy, it also has entropy that's log(1)=0. But since we rarely know the energy exactly and the energy levels may be extremely closely spaced, one typically "coarse grains" and defines the entropy as the log of the number of states within some range of energy, or with energy below some value, or by the energy of a canonical thermal ensemble (which is a distribution over energy states).

How does that fit in with the state model?

In other words if we are looking at the state of the universe, and a some system in that state has a given energy, entropy tells us which of the possible state transitions is likely to be taken, but how does energy contribute to determining which transitions are possible in the first place?

I mean, I am trying to wrap my head around why we can use energy to do work, in terms of states and transitions, given what we know about entropy and states and transitions.

 

[sol invictus]

How does that fit in with the state model?

In other words if we are looking at the state of the universe, and a some system in that state has a given energy, entropy tells us which of the possible state transitions is likely to be taken, but how does energy contribute to determining which transitions are possible in the first place?

If the total system has a certain definite energy, conservation of energy requires that the only possible transitions are to other states (if there are any) with exactly the same energy. In other words in the set of all states, conservation of energy defines a codimension one surface to which the system is restricted.

For a subsystem, conservation of energy doesn't necessarily restrict the possible transitions much (since energy can flow in and out). Still, if the system is fairly well isolated the energy can't change much, so it means the system will most likely transition to a state with higher entropy and roughly equal energy.

I mean, I am trying to wrap my head around why we can use energy to do work, in terms of states and transitions, given what we know about entropy and states and transitions.

Doing work in this language means lowering the entropy of a subsystem while raising the entropy of the rest of the system by more. For example, you can lower the entropy of a sandwich by putting it in your refrigerator, at the cost of raising the entropy of your kitchen by more. In the process you expended some energy - electric power in that case. You could get back some of that energy by using the sandwich-kitchen temperature difference to power a heat engine, but you'd never get back all of it (because some would go into "waste heat", in other words the entropy of the kitchen increased by more than the entropy of the sandwich decreased).

The whole process increases the total entropy, so it's consistent with our previous discussion. It's just that of all the processes starting from the same state that increase entropy by roughly the same amount, that one is a particularly nice one (at least if you like cold sandwiches).

 

[rocketdodger]

Is that really lowering the entropy of the sandwich?

It seems like there would be more low energy states than high ones, so a colder sandwich would in fact have higher entropy. Is this incorrect?