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In my opinion this is a high-importance subject. There are references to thermal fluctuations all over Wikipedia. RockMagnetist ( talk) 22:19, 17 September 2010 (UTC)
Beautiful lead section, Steve! I think this article is ready for promotion to Start. RockMagnetist ( talk) 13:04, 18 September 2010 (UTC)
I don't think it is correct to say that fluctuations are a source of dissipation. If you look at the fluctuation-dissipation theorem in the limit T → 0, you have no fluctuations yet you still have dissipation. I would say instead that both fluctuations and dissipation have a common source, which is the coupling of the system with the environment (a.k.a. thermal bath). -- Edgar.bonet ( talk) 13:50, 18 September 2010 (UTC)
This page needs to be renamed to thermal fluctuation. 70.247.166.5 ( talk) 01:08, 18 June 2012 (UTC)
It's perhaps worth pointing out the distinction between statistical fluctuations that occur from system to system within an ensemble, versus dynamic fluctuations ( stationary processes) that occur during the evolution of a single system. For very long times and in ergodic systems the two correspond. However, for short times the dynamic fluctuations can be much smaller than the statistical fluctuations, and in non-ergodic or weakly ergodic systems the dynamic fluctuations may even never reach the size of the statistical fluctuations, or require the lifetime of the universe to do so. When one uses language like "the system fluctuates around X" or "thermal fluctuations provide the energy necessary for the atoms to occasionally hop from one site to a neighboring one", one is referring to dynamic fluctuations on (implicitly) a prompt timescale. On the other hand, formulae like give the statistical fluctuation. Nanite ( talk) 14:18, 22 January 2014 (UTC)
Right before the application of central limit theorem, in the article, it says the moments are finite and therefore, we can expand f(E) around <E>, and the result is to the lowest order Gaussian.
It was not immediately obvious to me why the expansion results in Gaussian. After thinking for a while, I came to the following conclusion, which I'm not sure if it is exactly what the author meant to say or not: since E is the sum of order N contributions of approximately independent random variables (energies of individual degrees of freedom?), the central limit theorem applies, and therefore, f(E) is Gaussian?
Is that what it means or am I missing something? Can someone clarify the step where the expansion becomes Gaussian? Sprlzrd ( talk) 22:00, 10 April 2016 (UTC)
The inverse quantity in the Gaussian exponent must be replaced by the inverse matrix. See Landau, v5. Correct please who is better in English. Luksaz ( talk) —Preceding undated comment added 17:03, 6 June 2018 (UTC)
The article is quite technical and its fruition by a larger number of readers would be possible if it were made more self-contained. Thank-you — Preceding unsigned comment added by 2A01:E35:8AD5:C150:7CB7:94D4:6661:620 ( talk) 15:26, 3 February 2019 (UTC)
Max.kit and I disagree on whether angle brackets should be used around . The angle brackets refer to an average over the ensemble - something that should be clarified in the text - and is just another name for . Without the angle brackets, is just a variance for some unspecified state, not the energy dispersion for the system. RockMagnetist( talk) 18:45, 4 July 2020 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
In my opinion this is a high-importance subject. There are references to thermal fluctuations all over Wikipedia. RockMagnetist ( talk) 22:19, 17 September 2010 (UTC)
Beautiful lead section, Steve! I think this article is ready for promotion to Start. RockMagnetist ( talk) 13:04, 18 September 2010 (UTC)
I don't think it is correct to say that fluctuations are a source of dissipation. If you look at the fluctuation-dissipation theorem in the limit T → 0, you have no fluctuations yet you still have dissipation. I would say instead that both fluctuations and dissipation have a common source, which is the coupling of the system with the environment (a.k.a. thermal bath). -- Edgar.bonet ( talk) 13:50, 18 September 2010 (UTC)
This page needs to be renamed to thermal fluctuation. 70.247.166.5 ( talk) 01:08, 18 June 2012 (UTC)
It's perhaps worth pointing out the distinction between statistical fluctuations that occur from system to system within an ensemble, versus dynamic fluctuations ( stationary processes) that occur during the evolution of a single system. For very long times and in ergodic systems the two correspond. However, for short times the dynamic fluctuations can be much smaller than the statistical fluctuations, and in non-ergodic or weakly ergodic systems the dynamic fluctuations may even never reach the size of the statistical fluctuations, or require the lifetime of the universe to do so. When one uses language like "the system fluctuates around X" or "thermal fluctuations provide the energy necessary for the atoms to occasionally hop from one site to a neighboring one", one is referring to dynamic fluctuations on (implicitly) a prompt timescale. On the other hand, formulae like give the statistical fluctuation. Nanite ( talk) 14:18, 22 January 2014 (UTC)
Right before the application of central limit theorem, in the article, it says the moments are finite and therefore, we can expand f(E) around <E>, and the result is to the lowest order Gaussian.
It was not immediately obvious to me why the expansion results in Gaussian. After thinking for a while, I came to the following conclusion, which I'm not sure if it is exactly what the author meant to say or not: since E is the sum of order N contributions of approximately independent random variables (energies of individual degrees of freedom?), the central limit theorem applies, and therefore, f(E) is Gaussian?
Is that what it means or am I missing something? Can someone clarify the step where the expansion becomes Gaussian? Sprlzrd ( talk) 22:00, 10 April 2016 (UTC)
The inverse quantity in the Gaussian exponent must be replaced by the inverse matrix. See Landau, v5. Correct please who is better in English. Luksaz ( talk) —Preceding undated comment added 17:03, 6 June 2018 (UTC)
The article is quite technical and its fruition by a larger number of readers would be possible if it were made more self-contained. Thank-you — Preceding unsigned comment added by 2A01:E35:8AD5:C150:7CB7:94D4:6661:620 ( talk) 15:26, 3 February 2019 (UTC)
Max.kit and I disagree on whether angle brackets should be used around . The angle brackets refer to an average over the ensemble - something that should be clarified in the text - and is just another name for . Without the angle brackets, is just a variance for some unspecified state, not the energy dispersion for the system. RockMagnetist( talk) 18:45, 4 July 2020 (UTC)