Does a full 3TB hard drive weigh more than an empty one?

[Andy Resnick]

If I write a letter it could take me 3 hours and I'd burn 30 calories, however if I mail the letter to someone else doesn't mean I'm mailing them 3 hours of work and 30 calories.

no no no, the energy it took me to write the letter IS NOT carried with the letter, it stays in my room and all the calories are used to increase the internal energy in my room. The recipient of the letter gets not part of the calories I gave up in writing the message.

These statements are true. But I think you are confusing the energy required to write a letter with the free energy value of the information contained within the letter. Just because you expended 30 calories to write a letter doesn't mean your letter has 30/(kTln(2)) bits of information. I can't say how much information is in your letter without looking at it (making a copy).

 

[Mu naught]

It seems like there's a lot of hokus pokus going on in this thread.

 

[pallidin]

It seems like there's a lot of hokus pokus going on in this thread.

Don't rat me out.

 

[Curl]

These statements are true. But I think you are confusing the energy required to write a letter with the free energy value of the information contained within the letter. Just because you expended 30 calories to write a letter doesn't mean your letter has 30/(kTln(2)) bits of information. I can't say how much information is in your letter without looking at it (making a copy).

Okay, help me understand.

In Maxwell's Demon and Szilard's engine, the information the demon receives is all about the state of the particle(s) in the box. It is an instantaneous bit of information, and the reason it increases free energy is because it reverses the effect of entropy (information loss) by the random motion of the particle. It is similar to free-expanding a gas and then re-compressing it.

Keep in mind that the energy extracted (as a consequence of having information available) still comes from the surroundings, and in the case of Szilard's engine, it comes from "allowing the particle to expand back to its original volume", i.e. transferring momentum from the box walls to the particle.

So the information acquired by the demon simply reverses (partially) the information loss caused by an increase in entropy, which is why free energy can increase with that particular information.

However, I fail to see how a hard drive, who stores random bits, can count as entropy reversal. The data on the HD is not about any particular system, and it is also has no essence of time, which is crucial when you talk about information loss caused by increase in entropy. Even the wiki page itself states: "A neat physical thought-experiment demonstrating how just the possession of information might in principle have thermodynamic consequences". Even this type of information is not guaranteed to decrease entropy (and thus increase free energy).

 

[Andy Resnick]

Okay, help me understand.

In Maxwell's Demon and Szilard's engine, the information the demon receives is all about the state of the particle(s) in the box. It is an instantaneous bit of information, and the reason it increases free energy is because it reverses the effect of entropy (information loss) by the random motion of the particle. It is similar to free-expanding a gas and then re-compressing it.

<snip>

The data on the HD is not about any particular system

Really? the data on my hard drive definitely corresponds to specific things- experimental results, images of things, emails, music... What sort of data do you store on your HD?

 

[Andy Resnick]

Okay, help me understand.

I'm certainly willing to try- that's what PF is all about...

How much information is contained in your message? It depends on the message.

Let's say your letter, which cost you 30 cal to write, consists of 100 words of English text. If lossless transmission of your message means that I simply read the letter, then because on average English text has 10 bits per word

Mario C. Grignetti, A note on the entropy of words in printed English, Information and Control, Volume 7, Issue 3, September 1964, Pages 304-306, ISSN 0019-9958, DOI: 10.1016/S0019-9958(64)90326-2.
(http://www.sciencedirect.com/science/article/B7MFM-4DX496Y-P/2/2381c3d9d39a607e325a51df589865a2)

your message carries 1000*kTln(2) Joules of free energy. It may help to compare that to the 30 calories you expended writing it.

But perhaps you say "oh no- you need to know the detailed information about where every single atom of ink are on the page in order completely understand my message". This line of reasoning makes more sense when discussing the transmission of images: say your 30 calorie letter is a drawing of a Laue pattern. How much information does it now contain?

It could be quite a lot- there is a lot of information encoded in a far-field diffraction pattern. Diffraction is actually a very good compression scheme, but it's not lossless:

http://en.wikipedia.org/wiki/Phase_problem

 

[talk2glenn]

Andy, you cannot possible correlate the energy expended to do work (write a letter) with the information-value of the text on a page (one is subjective construct, the other is physical principle). There is no physical connection; these are entirely different concepts.

A message does not carry "energy", in a theoretical context (forgetting for a moment the energy content of its mass). The equivalence of terms (entropy in this case) is not intended to imply any equivalence of physics. Entropy means different things in an informative system, versus a physical one.

This is really quite silly.

Really? the data on my hard drive definitely corresponds to specific things- experimental results, images of things, emails, music... What sort of data do you store on your HD?

The universe could care less what you think you've stored on your HD. From a thermodynamic perspective, there is no difference between "ordered" and "random" data; the energy content is purely a question of the volume of massive particles, and has nothing to do with their order.

 

[Curl]

Really? the data on my hard drive definitely corresponds to specific things- experimental results, images of things, emails, music... What sort of data do you store on your HD?

The reason I'm confused is that I can't see how you can neglet the sense of time in these entropy calculations. It really bothers me to assign entropy values to any bit of information or even an English word, for example, as in the book you referenced.

I have a iittle thought experiment that might help you understand my source of confusion:

Consider Szilard's engine where, at some time, the demon gets the information "the particle is on the left". However, instead of closing the shutter/pistion and extracting kT*log(2) J of work, it simply eats some cake and comes back to work after a short break. At this point, the 1 bit of information that was given to the demon is still posessed by the demon (he didn't forget "the particle is on the left"). But, now the particle has moved and the kT*log(2) Joules of free energy are vanished, even though information is preserved... WHAT?

What I'm saying is that information is not directly equal to free energy, and it is not the case that any bit of information means entropy is decreased. Just like not all energy can do work, not all information can decrease entropy. Am I right?

 

[Andy Resnick]

The reason I'm confused is that I can't see how you can neglet the sense of time in these entropy calculations. It really bothers me to assign entropy values to any bit of information or even an English word, for example, as in the book you referenced.

I have a iittle thought experiment that might help you understand my source of confusion:

I'm not sure why you are bringing up 'time' all of a sudden, but it's not conceptually difficult to incorporate time into thermodynamics.

As for being 'bothered' that one can assign a quantitative amount of information to a word of English: there's not much I can do about that, other than to encourage you to keep learning until your conceptual conflict is resolved to your satisfaction.

Your thought experiment is flawed: the information about the system is then encoded in cupcakes: the number of cupcakes the demon ate is equal to the number of measurements taken. So the demon made an unauthorized copy of the information.

 

[diazona]

Ah, if only all information were encoded in cupcakes... :)

 

[Curl]

I'm not sure why you are bringing up 'time' all of a sudden, but it's not conceptually difficult to incorporate time into thermodynamics.

As for being 'bothered' that one can assign a quantitative amount of information to a word of English: there's not much I can do about that, other than to encourage you to keep learning until your conceptual conflict is resolved to your satisfaction.

Your thought experiment is flawed: the information about the system is then encoded in cupcakes: the number of cupcakes the demon ate is equal to the number of measurements taken. So the demon made an unauthorized copy of the information.

But the information about the particle (which could have yielded kT*log2 Joules of energy) is all of the sudden useless because the demon failed to act on the system in time. Thus the information is not destroyed, but becomes useless. This is why I don't understand how some declare that all information means decrease in entropy. This seems false, logically.

 

[Andy Resnick]

But the information about the particle (which could have yielded kT*log2 Joules of energy) is all of the sudden useless because the demon failed to act on the system in time. Thus the information is not destroyed, but becomes useless. This is why I don't understand how some declare that all information means decrease in entropy. This seems false, logically.

But the demon did *not* fail to act, unless the demon failed to eat a cupcake.

 

[Hellabyte]

If I define 'empty' as 'devoid of information' (i.e. all bits set to '0'), and 'full' as 'maximum information' (which would be a random string of 1's and 0's), then because there is a difference in entropy, there is a difference in total energy, and thus a difference in mass. The entropy per bit is kT ln(2), and from that you can calculate the change in mass.

I am very confused about the reasoning given here. Is the statement about the system having a different energy and therefore a different mass based on E=mc^2? The changing of 0s to 1s only affects the energy of the magnetic moment orientation. This doesn't have anything to do with the rest mass energy, or the rest mass associated with it...

I can't see how entropy can say anything one way or another about the mass of a system. Mass is not a thermodynamic quantity as far as I know.

 

[Andy Resnick]

I am very confused about the reasoning given here. Is the statement about the system having a different energy and therefore a different mass based on E=mc^2?

Yes.

The changing of 0s to 1s only affects the energy of the magnetic moment orientation. This doesn't have anything to do with the rest mass energy, or the rest mass associated with it...

Information is not the storage medium. Information is a way to quantify how far a message is from equilibrium.

 

[Hellabyte]

Yes.



Information is not the storage medium. Information is a way to quantify how far a message is from equilibrium.

To me, the usage of E=mc^2 is completely unfounded in this situation. It says that energy and mass can be converted into one another but just because a system has more "energy" that doesn't mean it has more mass. If i lift up a stone it has more gravitational potential energy, but it didn't gain any mass. You've given the magnetic dipoles more potential energy because of their orientation, but similarly the dipole doesn't gain any mass.