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The birth of statistical mechanics 
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#1
Feb1413, 02:31 AM

P: 935

This topic is about history of physics so I decided to post it in general physics section but it would be nice to have a history of physics(or maybe science)section.
Anyway,during my statistical mechanics course,I realized QM is being used from the beginning,in contrast to other parts of physics where a classical theory is developed first and then there are quantum corrections.So I wondered whether there was a time that there was classical statistical mechanics.I know,you now tell "of course there was" but by classical statistical mechanics I mean not considering energy levels and degeneracies and considering energy as a continuous parameter. I found Boltzmann's 1877 paper at http://www.trivialanomaly.com/ and took a look at it.In it,boltzmann assumes that particles can take velocities of the form [itex] \frac{p}{q} [/itex] and also he assumes that the energy(he uses the term "alive force" which I think he means energy)of any particle is an integer multiple of a constant factor. Also in http://arxiv.org/pdf/physics/9710007.pdf , it is said that Max Planck was inspired by Boltzmann's ideas in his theory about black body radiation. We know that maxwell independently had discovered maxwellboltzmann distribution.I wanna know had maxwell also have the idea of energy quantization or he just derived the distribution experimentally? Also I will appreciate any ideas about classical statistical mechanics and whether there is a distribution which considers energy as a continuous parameter. Thanks 


#2
Feb1413, 08:57 AM

HW Helper
P: 1,391

Yes, there is a "classical statistical mechanics" in which energy is considered as a continuous parameter  or, more precisely, energy is a function of the continuous state variables of position and momentum. However, it turns out that in order to write down sensible densities of states, etc., you need to bin the positions and momentum. The bin widths ##\Delta x## and ##\Delta p## end up entering into the density of states as the product ##\Delta x \Delta p##, so modern treatments tend to use our knowledge of quantum mechanics to identify this bin area with ##\hbar## (raised to the appropriate power if in 2 or 3 dimensions).
See, for example, sections 3.6 and 4.3.2 of Tobochnik and Gould, available online here: http://stp.clarku.edu/notes/ 


#3
Feb1413, 10:59 AM

P: 935

Yeah,my thoughts also led me to the result that classically,a particle has infinite number of choices for its energy content.So I concluded that for finding a classical energy distribution,a different approach should be taken.
Maybe we can tell that every energy between 0 and E is equally probable and probability distribution is 1/E. 


#4
Sep2513, 06:46 AM

P: 533

The birth of statistical mechanics
Statistical mechanics  Wikipedia, the free encyclopedia has a short history, mentioning several contributors who lived well before the discovery of quantum mechanics. Contributors like James Clerk Maxwell and Ludwig Boltzmann, who worked half a century before.
ETA: Gibbs paradox  Wikipedia, the free encyclopedia mentions the problem of what to do about phase space in the classical limit. It also mentions a problem with counting that quantum mechanics successfully resolves. Its discoverer, Josiah Willard Gibbs, Jr., had died in 1903. 


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