Timeline for Why does the expansion of gas into a vacuum mean that we have less information about the system? (entropy)
Current License: CC BY-SA 3.0
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| Feb 27, 2016 at 23:08 | vote | accept | whatwhatwhat | ||
| Feb 27, 2016 at 7:09 | answer | added | Bob Bee | timeline score: 1 | |
| Feb 27, 2016 at 4:23 | history | edited | whatwhatwhat |
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| Feb 27, 2016 at 4:22 | comment | added | whatwhatwhat | @CuriousOne Sounds a lot like entropy is the probability of a molecule being in a certain position. That would totally depend on the number of possible positions. | |
| Feb 27, 2016 at 4:08 | comment | added | CuriousOne | The one (current) state in which the system is, that would be information (which we don't have), the number of states that it could be in, that's enormous and that is what entropy expresses... how big is the to us irrelevant, potential amount of information that the system could represent, IF it could store information. We simply ignore that it can't and we count the potential states anyway because that number happens to have physical consequences. Unfortunately we are often talking about it as if represented actual information, which we shouldn't. | |
| Feb 27, 2016 at 4:02 | comment | added | CuriousOne | Quite the opposite. Look at it this one: one molecule and a tiny compartment in which it can't move. How many states that the system have? 1, right? The entropy of that is 0. Now double the volume. Now the molecule can be on one of two places. How much information can you store in that? 1 bit. Physicists call that an entropy of 1 (with a funny factor on top :-)). Now double the volume, again. Now the particle can be in one of four states. That's 2 bits and physicists assign an entropy of 2 (units). Add more particles, more volume, the numbers get bigger, but the principle stays the same. | |
| Feb 27, 2016 at 3:00 | comment | added | whatwhatwhat | @CuriousOne so the extra information is simply observing that the volume changed from $V_1$ to $V_2$? | |
| Feb 27, 2016 at 2:49 | comment | added | CuriousOne | It depends on how you define "information". Physicists have a somewhat quirky way of defining it. What they mean is that there are more places where the gas molecules can be after the volume expands, so there are more possible microscopic configurations. From an information theoretical perspective the volume/number of states is "potential information" or absence of information, if you like. You can look at it the other way round... it's an increase in the amount of information you would have to gather to completely describe an actual state of the gas. | |
| Feb 27, 2016 at 2:47 | history | edited | whatwhatwhat | CC BY-SA 3.0 |
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| Feb 27, 2016 at 2:46 | comment | added | whatwhatwhat | @TylerHG Yes, it can be defined in a general sense as the amount of disorder of a system. But the thing is that when the gas is on the left side only, it's still technically disordered because we don't know the exact position of every molecule in space. We only know in the macroscopic sense that the gas is on the left side. When we remove the partition, we know that the gas is now on both the left and right sides, but we still don't know the exact positions of every molecules in space. | |
| Feb 27, 2016 at 2:43 | comment | added | ClassicStyle | Do you know how entropy is defined? | |
| Feb 27, 2016 at 2:34 | history | asked | whatwhatwhat | CC BY-SA 3.0 |