History - Evolution of ideas in the field of thermodynamics (statistics in mechanical and gas dynamics)

[Ker_]

Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!

 

[Mister T]

I think Planck used the idea in a specific situation whereas Boltzmann used the idea in the general situation, providing a statistical explanation of the 2nd Law.

 

[gmax137]

I recently read the book "Boltzmann's Atom." It considers these questions. We had a brief discussion in this thread:

https://www.physicsforums.com/threads/what-are-you-reading-now-stem-only.912884/post-6929909

 

[vanhees71]

Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!

I'd say the very first having an idea of "kinetic theory" was Daniel Bernoulli, which has been taken up in more generality by Maxwell, as you say. Boltzmann's merit is to have derived the transport equation named after him and the discovery of the "H-theorem" ("Eta theorem"), which in modern formulation says that macroscopic entropy doesn't decrease, and equilibrium has thus to be a state of maximum entropy. The equation for the entropy in the microcanonial ensemble, ##S=-k \ln \Omega##, is indeed due to Max Planck.

The general equation, of course is (for classical statistics),
$$S=-k \int \mathrm{d}^3 x \mathrm{d}^3 p/h^3 f \ln(f/h^3).$$
Of course, Boltzmann couldn't know the quantum-theoretical choice of the "elementary one-particle phase-space cell" of volume ##h^3##, with ##h## Planck's quantum of action.

 

[Lord Jestocost]

Hi,
I have a question regarding the evolution of idea in the field of thermodynamics.
Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for the gas pressure). So why do we credit Boltzmann and not Maxwell for the "paternity" of statistics in mechanical and gas dynamics? What contribution did Boltzmann made that was so determinant?

Also, the equation s=klog(w) that is attributed to boltzmann... wasn't it Max Planck who actually wrote it down when working on his black body problem?

Thanks for helping me!

"Maxwell and Boltzmann worked on the kinetic theory of gases at about the same time in a slightly different manner and they achieved largely the same results, – all except one! That one result, which escaped Maxwell,
concerned entropy and its statistical or probabilistic interpretation. It provides a deep insight into the strategy of nature and explains irreversibility. That interpretation of entropy is Boltzmann’s greatest achievement, and it places him among the foremost scientists of all times."

From the book "A History of Thermodynamics" by Ingo Müller
https://link.springer.com/book/10.1007/978-3-540-46227-9