I haven’t reviewed it rigorously, but I’m a mathematician in a vaguely related domain and the proof outline seems plausible to me.
Prior work in https://arxiv.org/pdf/2408.07818 claims to prove that Boltzmann’s laws are the limit of a certain species of “hard sphere dynamics” as the number of particles gets large and the radius shrinks. This in the setting of unbounded Euclidean space. This is known classically for short time, which is why the 2024 paper purports to cover long time evolution.
The new preprint proves this result in the setting of a compact torus, which is more difficult because particles can collide an unbounded number of times. They seem to address this obstruction.
I give it a “more likely true than false; plausible even if there happen to be technical errors in the exposition.”
As for implications, eh, perhaps in some exotic systems. I suppose one could ask a similar question for magnetically driven particles and see if the answer was magnetohydrodynamics.
l0ng1nu5•9mo ago
Thanks for the response, I was kind of hoping it might have a bigger impact, perhaps in modelling of climate or weather.
inverted_flag•9mo ago
I wish people would stop posting links to SCMP, it’s a blatant propaganda rag. This article spends five sentences talking about the actual problem solved, and the rest is about the Chinese background of the authors, the Chinese social media reaction, and another unrelated Chinese mathematician who solved something. It doesn’t even link to the arxiv paper!
l0ng1nu5•9mo ago
TimorousBestie•9mo ago
This is the preprint in question.
I haven’t reviewed it rigorously, but I’m a mathematician in a vaguely related domain and the proof outline seems plausible to me.
Prior work in https://arxiv.org/pdf/2408.07818 claims to prove that Boltzmann’s laws are the limit of a certain species of “hard sphere dynamics” as the number of particles gets large and the radius shrinks. This in the setting of unbounded Euclidean space. This is known classically for short time, which is why the 2024 paper purports to cover long time evolution.
The new preprint proves this result in the setting of a compact torus, which is more difficult because particles can collide an unbounded number of times. They seem to address this obstruction.
I give it a “more likely true than false; plausible even if there happen to be technical errors in the exposition.”
As for implications, eh, perhaps in some exotic systems. I suppose one could ask a similar question for magnetically driven particles and see if the answer was magnetohydrodynamics.
l0ng1nu5•9mo ago