Recent content by Bill Dreiss

My corrected sentence clarifies the original but doesn't contradict it. On the other hand, Boltzmann is consistent throughout his writings from 1872 through 1895 in identifying equilibrium as the most probable macrostate (singular). If you can find an exception, please let me know...

While the notion that Boltzmann’s equilibrium includes nearby macrostates is widespread, it is not supported by the literature. Boltzmann is both explicit and consistent throughout his papers and his book Lectures on Gas Theory that equilibrium consists of a single macrostate (singular). For...

Kinetic theory, statistical thermodynamics

Correction. Boltzmann uses the isomorphic lottery example as the first step in his derivation of the entropy of the most probable macrostate. He references Maxwell on the velocity distribution.

You're right. Boltzmann focussed on the velocity/energy distribution and made no mention of the spatial distribution. However, most of the textbooks I've reviewed have presented the example of the number of molecules in one half of a box of gas as a teaching aid. Since this example relies on...

Thank you for the excellent reference. The paper is a welcome corroboration of my ideas, as indicated by the following quotes: Page 2: This means that there will be no convergence to an attractor (which could in the dynamic sense be taken as an equilibrium state). [This negates Boltzmann’s...

It seems impossible to exactly reverse the motion of the particles for a real gas due to the butterfly effect and the fact that the average molecule moves at about half a kilometer per second at room temperature. In place of speculating on the hypothetical results of such an experiment, we can...

The simulation I linked to displays the molecular distribution in space. The energy distribution is a separate problem. Everthing I've said so far has been related to the spatial distribution, which is generally what we observe in real life. I'm not saying that you rerun the simulation from...

As near as I can tell, this idea was first proposed by William Thompson in the paper “The Kinetic Theory of the Dissipation of Energy” (1874), which can be found in The Kinetic Theory of Gases by Stephen G. Brush. (see the highlighted text in the attachment) It's possible that this is where...

Here's someone else who gets it: https://www.physicsforums.com/threads/loschmidts-paradox-and-free-gas-expansion.1010383/

I believe the following is consistent with your post. In section 52-2 of The Feynman Lectures on Physics, Vol. 1, Feynman says, “Next we mention a very interesting symmetry which is obviously false, i.e., reversibility in time. The physical laws apparently cannot be reversible in time, because...

As near as I can tell, Boltzmann's insight was first proposed by William Thompson in the paper “The Kinetic Theory of the Dissipation of Energy” (1874), which can be found in The Kinetic Theory of Gases by Stephen G. Brush. (see the highlighted text in the attachment) It's possible that this is...

I don't either, since the process he's describing is deteministic.

The essence of science when you encounter something hard to understand is to think.

My observations involve kinetic theory, which preceded statistical mechanics. Feynman's line of reasoning was identical to mine and he would have reached the same conclusion as I did if he had not made a careless mistake. The crutial observation which leads to this conclusion is that if the...