The birth of statistical mechanics

[ShayanJ]

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 $\frac{p}{q}$ 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 maxwell-boltzmann distribution.I want to 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

 

[Mute]

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/

 

[ShayanJ]

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.

 

[lpetrich]

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.

 

[LudusRex]

I find the topic of the birth of statistical mechanics to be fascinating and important in understanding the development of physics as a whole. It is interesting to note that quantum mechanics has been used from the beginning in this field, unlike other areas of physics where classical theories were first developed and then later modified with quantum corrections. This raises the question of whether there was a time when classical statistical mechanics existed, without taking into account energy levels and degeneracies.

Upon further investigation, I found that Boltzmann's 1877 paper indeed addressed this issue by assuming that particles can have velocities of the form \frac{p}{q} and that their energy, which he refers to as "alive force", is a multiple of a constant factor. This suggests that even in the early days of statistical mechanics, there was an understanding of energy quantization. It is also interesting to note that Max Planck, who is known for his famous theory about black body radiation, was inspired by Boltzmann's ideas.

In regards to Maxwell, it appears that he independently discovered the Maxwell-Boltzmann distribution, which takes into account the energy levels of particles. It is unclear whether he also had the idea of energy quantization or if he derived the distribution experimentally.

Overall, it seems that classical statistical mechanics did consider energy as a continuous parameter, but the concept of energy quantization was also present in the early stages of this field. It is a testament to the interconnectedness and evolution of scientific ideas, as Boltzmann's and Planck's work laid the foundation for the development of quantum mechanics. Thank you for bringing up this interesting topic and I hope to continue exploring the history of physics in the future.