Heat Transfer and Scientific Reasoning

[Jagella]

Hello, friends:

I just got done studying a chapter in a physics text that explains how heat transfers from higher-temperature objects to lower-temperature objects. Unfortunately, that chapter said little about why heat transfers from higher-temperature objects to lower-temperature objects, so naturally I set out to answer that question.

On the macro level, a hotter object in contact with a cooler object will cool while the cooler object will warm up. After some time, the two objects will be the same temperature, and heat exchange will cease. I decided to consider what might be happening at the molecular level. Realizing that the energy levels of molecules vary directly with temperature, I concluded that the molecules in the hotter object must have higher energy levels than the molecules in the cooler object. How might energy be transferred between molecules?

To answer this question, I decided to focus on the simplest system I can think of: two molecules of different energy levels. If a molecule of higher energy, like the molecule of a hot object, comes into contact with a lower-energy molecule like that in a cooler object, then energy is evidently exchanged between the two molecules. Since the hot molecule's energy is the greater of the two, its energy “overcomes” the energy of the cooler molecule, but only to an extant. The energy of the cool molecule “resists” the hot molecule's energy which lessens the energy of the hot molecule. The hot molecule's energy, on the other hand, increases the energy of the cooler molecule. The net effect is that the two molecules acquire an amount of energy that is about equal.

If we zoom out back to the macro level, the trillions of molecules in the two objects are undergoing the kind of process I just described for two molecules. Thermal energy moves from trillions of hot molecule to trillions of cooler molecules. We experience this movement of energy as heat transfer or an increase in temperature in the hotter object and a decrease in energy and in temperature in the cooler object. Once the molecules' energy levels are about the same, heat transfer stops.

A mechanical analogy may help to clarify the process of heat transfer on the molecular level. Say a car moving at 50 miles per hour is rear-ended by a truck moving at 60 miles per hour. If neither vehicle is damaged to the extent that they would slow down from friction, then the car would speed up while the truck might slow down a bit. Some of the truck's kinetic energy is transferred to the car increasing the car's energy while the truck's energy decreases by that same amount of energy. More energy for the car increases its speed; less energy for the truck decreases its speed. Molecules exchange energy in a similar fashion.

Am I right or wrong about what accounts for heat transfer? At this point you may agree or disagree with what I'm saying. Whether I'm right or wrong is not terribly important to the point I'm trying to make. I'm trying to demonstrate basic reasoning that should be useful in answering scientific questions.

I'd appreciate some feedback on this issue.

Jagella

 

[Mapes]

Hi Jagella,

Thanks for posting this, I enjoyed reading it. These comments are intended to spark thought about the reasoning process:

- What does it mean for a higher-energy molecule to "overcome" the lower-energy molecule? It is hard to visualize what is happening physically here.

- Why do the two molecules need to end up with a temperature that is "about equal"? Conservation of energy would still be satisfied if the higher-energy molecule gained energy and the lower-energy molecule lost it. Essentially, the question still exists, although on a molecular level now, of why hotter objects heat colder objects.

- In this model, all the molecules of a substance have approximately the same energy level. Is this necessary? Could they have a distribution of energy levels, with the mean or median being higher for the hotter object?

- How do we explain radiative heat transfer through a vacuum, in which hotter objects also heat colder objects? No molecular contact exists here.

 

[atyy]

What is a hot molecule?

 

[harrylin]

Hello, friends:

I just got done studying a chapter in a physics text that explains how heat transfers from higher-temperature objects to lower-temperature objects. Unfortunately, that chapter said little about why heat transfers from higher-temperature objects to lower-temperature objects, so naturally I set out to answer that question.
[..]
A mechanical analogy may help to clarify the process of heat transfer on the molecular level. Say a car moving at 50 miles per hour is rear-ended by a truck moving at 60 miles per hour. If neither vehicle is damaged to the extent that they would slow down from friction, then the car would speed up while the truck might slow down a bit. Some of the truck's kinetic energy is transferred to the car increasing the car's energy while the truck's energy decreases by that same amount of energy. More energy for the car increases its speed; less energy for the truck decreases its speed. Molecules exchange energy in a similar fashion.

Am I right or wrong about what accounts for heat transfer? At this point you may agree or disagree with what I'm saying. Whether I'm right or wrong is not terribly important to the point I'm trying to make. I'm trying to demonstrate basic reasoning that should be useful in answering scientific questions.

I'd appreciate some feedback on this issue.

Jagella

I think that your ideas go in the right direction; however there should be no damage to gas molecules; the collitions must be elastic.

For more, you could search the internet for "Kinetic Molecular Theory of gases", or start with the introduction here:
http://en.wikipedia.org/wiki/Kinetic_theory

For the same in a more advanced form, you can also have a look at Statistical Mechanics:
http://bayes.wustl.edu/etj/articles/theory.1.pdfHarald

 

[Jagella]

Thanks for posting this, I enjoyed reading it.

And thank you for the response.

What does it mean for a higher-energy molecule to "overcome" the lower-energy molecule? It is hard to visualize what is happening physically here.

It's interesting that you should ask about what I meant by “overcome” and how to visualize it. I had some problem there, too, and I realize that to say that one energy level overcomes another, lesser energy level is a bit vague. I used my drawing software to draw two molecules represented by circles, and I drew arrows coming from each molecule. The length of the arrows represents the amount of energy each molecule has. Longer arrows represent greater energy levels. When two molecules exchange some energy in a collision, the more energetic molecule will make the the lower-energy molecule move faster while the higher-energy molecule will move more slowly. I then redrew the molecules with arrows of equal length representing these equal energy levels. That's what I meant by “overcome.”

By the way, using drawing software is a great way to visualize and understand concepts in physics, mathematics, and other disciplines.

Why do the two molecules need to end up with a temperature that is "about equal"? Conservation of energy would still be satisfied if the higher-energy molecule gained energy and the lower-energy molecule lost it. Essentially, the question still exists, although on a molecular level now, of why hotter objects heat colder objects.

In a collision between two molecules, the higher-energy molecule will normally lose energy while the lower-energy molecule will tend to gain the same amount energy the other molecule loses. The higher-energy molecule gives the lower-energy molecule a push increasing the other molecule's energy and decreasing its own energy. This process brings the two energy levels closer in magnitude. This “zero-sum game” is a result of the conservation of energy.

I understand it's possible for the higher-energy molecule to gain energy from a collision while the lower-energy molecule loses energy, but such an exchange is very unlikely. I think that if the two molecules are moving in the same general direction, then the lower-energy molecule might bump the higher-energy molecule from behind. In that case, the higher-energy molecule would gain energy while the lower-energy molecule would lose energy. If this situation happened for most of the molecules in two objects, then the hotter object would get hotter while the colder object got colder! This result is extremely unlikely, though.

In this model, all the molecules of a substance have approximately the same energy level. Is this necessary?

No. Heat transfer takes time. Prior to the time at which thermal equilibrium takes place, an object may have higher-energy-level molecules on one side and lower-energy-level molecules on the other side.

Could they have a distribution of energy levels, with the mean or median being higher for the hotter object?

Sure. If the energy levels of the molecules are randomly distributed, then most of the molecules in an object will have an energy level close to the mean value. If another object is colder, a similar distribution of molecular-energy levels should be present, but the mean value will be lower than the hotter object's mean value, of course.

How do we explain radiative heat transfer through a vacuum, in which hotter objects also heat colder objects? No molecular contact exists here.

In that case heat is transferred via electromagnetic radiation which, unlike heat conduction or convection, needs to substance to move through. I'm not sure, but I believe this kind of heat transfer occurs through the fabric of space as described in Einstein's General Theory of Relativity.

I am, admittedly, a little shaky on that last point.

Jagella

 

[Jagella]

What is a hot molecule?

A "hot" molecule is a molecule that has a higher energy level than other molecules it comes into contact with. I was a bit vague in using that term, and I'm glad you asked for a clarification.

Jagella

 

[Jagella]

For more, you could search the internet for "Kinetic Molecular Theory of gases", or start with the introduction here:

Thanks for the advice and the link, but I'll need to read it later. At this point I'm more concerned with basic reasoning than with research. I could have looked up the answer to why heat transfers from hot to cold easily enough, but I'm trying to come up with the answers myself. That way I hope to be able to discover things that nobody else knows.

Jagella

 

[atyy]

A "hot" molecule is a molecule that has a higher energy level than other molecules it comes into contact with. I was a bit vague in using that term, and I'm glad you asked for a clarification.

Jagella

Higher kinetic energy?

Let's say your procedure works. Now take the "final" state and reverse the directions of all velocities. The "reverse" collisions should still satisfy Newton's laws, and produce the initial state. No?

 

[Drakkith]

Thanks for the advice and the link, but I'll need to read it later. At this point I'm more concerned with basic reasoning than with research. I could have looked up the answer to why heat transfers from hot to cold easily enough, but I'm trying to come up with the answers myself. That way I hope to be able to discover things that nobody else knows.

Jagella

That isn't the way science works. You are effectively stuck in the 1800's and trying to come up with the kinetic theory of gases yourself. We already know what happens, and if you think you are going to find something that thousands upon thousands of people have missed somehow, then you are sorely mistaken and wasting time. And you have a much much better chance of finding something new if you understand the theory anyways. How can you find something new if you don't even know what is and isn't true in the first place?

 

[Jagella]

Higher kinetic energy?

Let's say your procedure works. Now take the "final" state and reverse the directions of all velocities. The "reverse" collisions should still satisfy Newton's laws, and produce the initial state. No?

I don't believe merely reversing the directions of the molecules' motions can restore the initial state. In my rationale, the magnitude of each molecule's energy comes into play more than the direction of motion. To restore the initial state, the energy levels of the molecules would need to be reset to their initial values.

That's an interesting question. Why do you ask?

Jagella

 

[Jagella]

That isn't the way science works. You are effectively stuck in the 1800's and trying to come up with the kinetic theory of gases yourself. We already know what happens, and if you think you are going to find something that thousands upon thousands of people have missed somehow, then you are sorely mistaken and wasting time. And you have a much much better chance of finding something new if you understand the theory anyways. How can you find something new if you don't even know what is and isn't true in the first place?

I think you misunderstand what I said. I didn't mean that I would discover something new about heat transfer; I meant that I might discover something new about something that is not yet well understood.

What inspired my posting my initial comments is my recently learning about how Einstein came up with a theory that explains the photoelectric effect. Rather than trying to explain the photoelectric effect as being the result of wave motion, Einstein posited that light is made up of particles or photons. Photons strike the electrons in the metal, and the energy of the photons, understood as their frequency, impart the same frequency to the electrons they collide with. Einstein won the Nobel prize for this work.

How did Einstein do it? It seems to me that his independent thinking enabled him to see things other physicists didn't see. He thought "out of the box," and outside of the box is where new knowledge resides waiting to be discovered.

And as far as finding something new about heat transfer, I don't believe it hurts to take a look. History has demonstrated more than once that "thousands upon thousands" have missed discoveries. Ever hear of Copernicus? Da Vinci? Newton? Darwin?

Jagella

 

[atyy]

I don't believe merely reversing the directions of the molecules' motions can restore the initial state. In my rationale, the magnitude of each molecule's energy comes into play more than the direction of motion. To restore the initial state, the energy levels of the molecules would need to be reset to their initial values.

That's an interesting question. Why do you ask?

Jagella

Heat transfer is irreversible in time - you cannot get heat transferred from a cold object to a hot object by placing them next to each other. However, the laws of physics are reversible in time (with one exception, not relevant to this discussion). So the direction of heat transfer should not be derivable from the laws of physics. To take your truck and car example, there is no law of physics which says that the car cannot go backwards and front end a truck, causing the truck to start moving. It just so happens that the way the universe is set up (at the "beginning of time"), we see heat transfer in only one direction.

 

[harrylin]

Thanks for the advice and the link, but I'll need to read it later. At this point I'm more concerned with basic reasoning than with research. I could have looked up the answer to why heat transfers from hot to cold easily enough, but I'm trying to come up with the answers myself. That way I hope to be able to discover things that nobody else knows.

Jagella

That would be a good idea if the current theory was, as you probably thought, undeveloped or unsatisfactory. However, it's not very useful to try to reinvent the wheel. :tongue2:

Meanwhile you received the feedback that you demanded: that type of scientific reasoning did lead to a highly satisfying theory.


Harald

 

[harrylin]

[..] So the direction of heat transfer should not be derivable from the laws of physics. [..] It just so happens that the way the universe is set up (at the "beginning of time"), we see heat transfer in only one direction.

I think that that puzzle has been solved (derived from combining the laws of physics with logical reasoning), as also indicated in the second reference that I gave.Harald

 

[atyy]

I think that that puzzle has been solved (derived from combining the laws of physics with logical reasoning), as also indicated in the second reference that I gave.


Harald

It depends on whether initial conditions are included in the "laws of physics".

 

[cshum00]

Heat transfer is irreversible in time - you cannot get heat transferred from a cold object to a hot object by placing them next to each other. However, the laws of physics are reversible in time (with one exception, not relevant to this discussion).

I am sorry. Can you explain your statements a little further. I am confused because i think you are mixing two unrelated things together (time and heat transfer).

What the law of thermodynamics dictates is that heat transfer only occurs from a objects of higher kinetic energies to objects with lower kinetic energies. Nothing to do with time as far as i understand.

Then there is time in physics, which you say is irreversible? In which you are mixing up heat with time travel?

 

[atyy]

I am sorry. Can you explain your statements a little further. I am confused because i think you are mixing two unrelated things together (time and heat transfer).

What the law of thermodynamics dictates is that heat transfer only occurs from a objects of higher kinetic energies to objects with lower kinetic energies. Nothing to do with time as far as i understand.

Then there is time in physics, which you say is irreversible? In which you are mixing up heat with time travel?

Oh, I just mean something very naive. The second law of thermodynamics means heat flows from hot to cold. So if we see cold to hot, we assume time is running backwards, so as not to violate the second law. However, apart from the second law of thermodynamics, no other law of physics (with one irrelevant exception) prohibits the time-reversed version of a process from going forward in time.

 

[cshum00]

I see where you guys are going and why time and vectors were introduced into the topic.

Let's say your procedure works. Now take the "final" state and reverse the directions of all velocities. The "reverse" collisions should still satisfy Newton's laws, and produce the initial state. No?

However, apart from the second law of thermodynamics, no other law of physics (with one irrelevant exception) prohibits the time-reversed version of a process from going forward in time.

So quick answer to your question is Yes.

I see from your two previous posts you are aiming for a revert the collision events that is why you included vectors and time. As you may already know, to revert a process, we must take into account the proper parameters and revert them accordingly in the right order.
-Reverting only the directions without taking account the position at the given time will just create a new unrelated event.
-Only reverting the time without reversing the vectors will just be a backward-playback of the original event.

For the sake of the argument we will only use only one dimension:
-Particle A sits on x=0m at t=0s with v(i)=4m/s
-Particle B sits on x=4m at t=0 with v(i)=2m/s
-For particle A at t=1s, x=4m, v=4m/s
-For particle B at t=1s, x=6m, v=2m/s
-For particle A at t=2s, x=8m, v=2.1m/s
-For particle B at t=2s, x=8m, v=3.9m/s
-For particle A at t>2s, v=2.1m/s
-For particle B at t>2s, v=3.9m/s

..A>>B>...   t=0s
..A...B...   t=0s
...A.B...   t=1s
...AB...   t=2s
...A..B..   t=3s
...A>.B>>   t=3s

As you can see, the collision happens at t=2s.

Now if we revert the process:
-For particle B at t>2s, v=-3.9m/s
-For particle A at t>2s, v=-2.1m/s
-For particle B at t=2s, x=8m, v=-3.9m/s
-For particle A at t=2s, x=8m, v=-2.1m/s
-For particle B at t=1s, x=6m, v=-2m/s
-For particle A at t=1s, x=4m, v=-4m/s
-For particle B at t=0s, x=4m, v=-2m/s
-For particle A at t=0s, x=0m, v=-4m/s

...<A<<B..   t=3s
...A..B..   t=3s
...AB...   t=2s
...A.B...   t=1s
..A...B...   t=0s
<<A..<B...   t=0s

Explaining heat transfer with particle collisions can be held true (without breaking the second law of thermodynamics) only if the following conditions are present:
(1) If two particles of different kinetic energies collide, the resultant energy inside each particle must be closer to their average.
(2) If two particles of the same kinetic energies collide, the collision must be completely elastic.

Which becomes the new mysteries:
(1) Why the resultant collision must be closer to their averages?
(2) Why when particles have the same kinetic energies their collision becomes completely elastic? For example, can't two particles of same magnitude but opposite direction collide and result on a completely inelastic collision where both particles are put into halt?

Edit: A possible explanation to (1) is because particles are aiming for completely elastic condition (2). But then we are stuck on why they aim for completely elastic collision.

 

[atyy]

Edit: A possible explanation to (1) is because particles are aiming for completely elastic condition (2). But then we are stuck on why they aim for completely elastic collision.

It should be ok to use only elastic collisions. Fundamentally all interactions conserve energy. Let's assume the gas is pretty dilute, so most of the the time the inter-particle distances are large. We can assume that the potential energy falls off with inter-particle distance, so that at large inter-particle distances all the energy is kinetic. So conservation of energy is the same as conservation of kinetic energy.

However, I still think that would not explain why the reversed collisions cannot take place.

 

[cshum00]

It should be ok to use only elastic collisions. Fundamentally all interactions conserve energy. Let's assume the gas is pretty dilute, so most of the the time the inter-particle distances are large. We can assume that the potential energy falls off with inter-particle distance, so that at large inter-particle distances all the energy is kinetic. So conservation of energy is the same as conservation of kinetic energy.

I guess i only complicated things by creating the second statement.

However, I still think that would not explain why the reversed collisions cannot take place.

I guess i forgot to explain some of the results of the example i presented before.
-As you can see, by the time we reverse the process; the energy contents have already been swapped as well.
-Originally particle A had more energy than particle B. After the collision, particle B had more energy than particle A.
-So when we reverted the process, B had more content than particle A to begin with. Meaning that energy is still transferred from higher to lower energy content regardless.
(Of course, my example is only valid if particle A and B had the same mass)

Again, that goes back to statement (1) where we only allow energy of high energy objects to be transferred to lower energy objects. If we allow low energy content to become a lower energy content while transferring the energy to a higher energy content this explanation collapses. Because if statement (1) does not hold true, then even if we revert the process; then energy content will still be transferred from lower energy to higher energy contents.

Edit: By the way, even in collisions, it is hard to imagine an object with little momentum to transfer energy to a object with higher momentum. The example would be an object metting another object at a 90 degree angle.

A>>..
...^
...B

 

[Drakkith]

How did Einstein do it? It seems to me that his independent thinking enabled him to see things other physicists didn't see. He thought "out of the box," and outside of the box is where new knowledge resides waiting to be discovered.

And as far as finding something new about heat transfer, I don't believe it hurts to take a look. History has demonstrated more than once that "thousands upon thousands" have missed discoveries. Ever hear of Copernicus? Da Vinci? Newton? Darwin?

Jagella

None of them ever tackled a problem by NOT learning about the current theories at the time. What it looks like to me, is that you are trying to come up with new Football strategy without even knowing the rules of the game. Eintstein approached a known problem that could not be explain by current understanding of the day. He did not go back and look at everything learned about the wave nature of light and simply discover something new. You are NOT thinking outside the box, as you aren't even in the mailroom.

Furthermore, the overwhelming majority of discoveries happen because someone applies themselves to a known problem, examines all available evidence, applies critical thinking, and through the scientific method comes up with a new theory. Even the "accidental" discoveries are usually a result of related research or development. Einsteins discoveries, while very important and extremely influential, did not come about solely because he "thought outside the box". He took equations and ideas from several different people and put them together when he developed the Photoelectric effect and Relativity.

You MUST learn about known science first, otherwise how would you even know if you were right or wrong? Or even recognize a real problem when you see it? Your initial posts seemed to suggest you understand at least a little bit about the issue, so it would be just another step to understand the kinetic theory and other related concepts.

Put simply, new knowledge is not located outside the box. It is merely hidden inside waiting to be found. You have to know how to open the box before you can get to the knowledge inside.

 

[cshum00]

I found the loophole in my example. In my example i have particle A with higher energy content than particle B before the collision. But after the collision i swapped which would have more energy content.

The loophole has to be presented at least on a 2D or 3D dimension. What if particle A starts with higher energy content and still have higher energy content after the collision. In that case statement (1) won't hold true anymore. Because if we revert the process, B with less energy contents will collide with particle A and pass on energy from a lower kinetic particle to a higher one.

 

[Jagella]

That would be a good idea if the current theory was, as you probably thought, undeveloped or unsatisfactory. However, it's not very useful to try to reinvent the wheel.

Hi Harry:

I'm glad you brought up this issue because I'm wondering if some of the basic physics taught in the physics curriculum at universities is “fully developed.” Has all the work been done on the physics of sound, optics, motion, force, and of course heat transfer and thermodynamics? I can't say I share your assurance that we know all there is to know about these fields of study. The history of science testifies to the paradigm shifts in science that occur periodically. Copernicus and Einstein are two examples of great minds that demonstrated that we are still learning about the world we live in, and we should never be too sure that we “have it.”

As for “reinventing the wheel,” I agree that we need not reinvent the wheel if we merely want wheels, but if we want to know what the invention process involves, then reinventing the wheel or rediscovering why heat moves from cold to hot can be very enlightening. That's why students in physics labs to this day perform Young's two-slit experiment: they need to learn how to discover.

Jagella

 

[atyy]

High recommended: http://www.youtube.com/watch?v=2OU_f7vYDys&feature=related

Also: http://www.youtube.com/watch?v=tGrsK4PVgsM&feature=related, especially 6:00 to 7:15

Full lecture is at: http://research.microsoft.com/apps/tools/tuva/index.HTML#data=3|||

 

[cshum00]

@atyy
Really nice video. I really liked how Feynman explained that certain process are irreversible because of the specific conditions our universe has; which favor certain outcomes. And in order to create the reversible process, we would actually have to create special conditions isolated and independent from our universe.

It reminds me on how the the air conditioner works. We can cool air with special conditions by inputting work but it only works inside a sealed compartment. Even then, because the air conditioner is inside the universe we live in; inputting work actually it increases the amount of total heat produced and dumped onto the environment.

 

[harrylin]

It depends on whether initial conditions are included in the "laws of physics".

Laws of physics relate to those: They predict what future conditions will be as based on current conditions.

 

[harrylin]

Hi Harry:

[..] I can't say I share your assurance that we know all there is to know about these fields of study. [..]

I did not even suggest such a thing!

As for “reinventing the wheel,” I agree that we need not reinvent the wheel if we merely want wheels, but if we want to know what the invention process involves, then reinventing the wheel or rediscovering why heat moves from cold to hot can be very enlightening. That's why students in physics labs to this day perform Young's two-slit experiment: they need to learn how to discover.
Jagella

Students in physics labs rarely, if ever, get to perform Young's experiment without first getting any knowledge about it. I agree that it's necessary to do your own thinking, but as you already did that (or else, after a little extra trying), you would do well to compare your work with what has already been done by others. In general you can learn a lot from existing inventions.

 

[Jagella]

Students in physics labs rarely, if ever, get to perform Young's experiment without first getting any knowledge about it.

Of course I understand that most educational institutions teach the basics first and then move on to more advanced topics. I've found that the opposite approach can be very effective. For instance, I'm currently studying a physics text backwards. I study a chapter and then move on to the previous chapter. By studying this way, I have a lot of unanswered questions on my mind. The longer I ask those questions, the better I seem to understand the answers when I finally get the answers. I'm not sure if I'd recommend this approach to everybody, but it seems to work for me.

I agree that it's necessary to do your own thinking, but as you already did that (or else, after a little extra trying), you would do well to compare your work with what has already been done by others. In general you can learn a lot from existing inventions.

Yes. I've found that all great thinkers borrow a lot of their thinking from others. As Newton said: “I see as far as I do because I stand on the shoulders of giants.”

Jagella

 

[atyy]

For more, you could search the internet for "Kinetic Molecular Theory of gases", or start with the introduction here:
http://en.wikipedia.org/wiki/Kinetic_theory

For the same in a more advanced form, you can also have a look at Statistical Mechanics:
http://bayes.wustl.edu/etj/articles/theory.1.pdf

I think that that puzzle has been solved (derived from combining the laws of physics with logical reasoning), as also indicated in the second reference that I gave.

Laws of physics relate to those: They predict what future conditions will be as based on current conditions.

I just noticed your second link actually does not give the answer "initial conditions". It gives something about our "state of knowledge". I'm not sure Jaynes's view is entirely satisfactory, since the final state of a system should depend on dynamics. We do know some systems that do not reach "thermal equilibrium" for some initial conditions, so Jaynes's view is at least incomplete http://arxiv.org/abs/1007.3957. However, I believe it is true the increase of entropy depends both on initial conditions and a lack of knowledge. An example is Landau damping, where for some initial conditions, the energy gets transported into higher and higher frequencies, which are beyond the range of our measurement, and so that a non-dissipative process appears to be dissipative http://fr.arxiv.org/abs/0904.2760. However, Jaynes is an influential figure, so perhaps not everyone will agree.