Timeline for Entropy - Gas Inside A Closed System Reaches Maximum Entropy
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 5, 2015 at 6:17 | vote | accept | pZombie | ||
| Apr 20, 2015 at 9:22 | comment | added | gatsu | Also, there are multiple entropies and not only a single one. If you consider a gas in a box at equilibrium and at a given (E,N,V) then it has a unique value for its Gibbs entropy $S_G = k_B \ln \Omega_{tot}$. Now, you can also look at configuration entropies which, to a given macro observable $x$ associate a partial entropy $S(x) = k_B \ln \Omega(x)$ such that $\sum_x \Omega(x) = \Omega_{tot}$. You can look for the most probable value for $x$ which happens to maximize $S(x)$ and you recover an effective entropy maximization criterion. However, the variable $x$ can still vary and fluctuate. | |
| Apr 20, 2015 at 9:15 | comment | added | gatsu | Yes, exactly. In practice, if you see just a single system with all its particles in a corner of a box, you cannot tell whether it is at equilibrium or out of it. Equilibrium means equilibrium statistics. Only when the statistical fluctuations are negligible (for very big systems) can you only worry about average values without carrying about fluctuations. | |
| Apr 20, 2015 at 8:27 | comment | added | pZombie | OR differently put once again... You would not be able to tell apart a closed system which has reached that "equilibrium state" and then fluctuated largely about it to a certain entropy state from a system which never reached that "equilibrium state" but happens to have arrived at a similar entropy state like the former (post fluctuations) system. So the meaning of remaining at the equilibrium state forever seems non-existent. | |
| Apr 20, 2015 at 8:22 | comment | added | pZombie | To be more precise. This "equilibrium state" does not really answer the question. It rather conceals it. It's not a fixed entropy state of a system, but rather seems to describe an entropy state of the system around which the system wiggles about (fluctuations). Those fluctuations can be so large, the system could, given enough time, fall back to it's initial state. Yet you would call this a system being in equilibrium forever still, suggesting that the system is fixed somehow when it is not. | |
| Apr 20, 2015 at 8:12 | comment | added | pZombie | I find this to be a horrible description. First of all, is the equilibrium state equal to the maximum entropy state OR is it the state i pondered below, where the likeliness of the closed system's entropy to increase is equal to the probability of it decreasing? And then while you say it will stay in this equilibrium state forever, you bring up fluctuations at the same time which basically means that it does NOT stay in this state forever. Also, you do not quantify how large those fluctuations can be, given you waited a very long long time. Maybe it can fluctuate back to even min entropy? | |
| Apr 20, 2015 at 7:37 | history | answered | gatsu | CC BY-SA 3.0 |