Boltzmann's Entropy Equation: A History from Clausius to Planck

Boltzmann's entropy formula was created by Max Planck in 1900! So, why did Planck create this equation and how did it end up on Boltzmann's grave? I used primary sources to explain the history of this famous and confusing equation.

My Patreon Page (thanks!):

[thomassynths]

Correction: `log` is a transcendental function, not a trigonometric function. (Side note: all the trig funcs are transcendental.) Transcendental means that the function cannot be described by a polynomial.

[pieteruys]

As a student one of the subjects in my final undergraduate year was Statistical Mechanics. I was hugely impressed by the sheer brilliance of the reasoning involved. it is an intellectual tour de force. Thank you for presenting this history

[sonarbangla]

Extremely beautifully and masterfully explained by Kathy. Why Plank's equation was engraved on Boltzmann's tomb stone is one of paying respect out of indebtedness on the part of Plank, perhaps saddened by the death of a great man and teacher. Kathy you video sounded like music to my ears. Thank you.

[jackd.ripper]

Bassi.
You are just friggin' awesome. The most underrated channel on YouTube.

[anonymous.youtuber]

Thanks for these very interesting stories. So often the historical context is missing from the teachings, which is a pity because it makes the study of science so much more colorful.
It really struck me that the quantization concept emanated from kinetic gas theory, up until now I was made to believe it was only considered to explain the discrete character of spectral lines in relation to atomic theory.
Your videos are so enlightening. Respect !

[profjoshtan]

From watching this, I have come to appreciate for the first time why we focus on Boltzmann's H-theorem in spite of it not quite doing what many physics teachers who teach it claim it does. In classes where the H-theorem is taught, it is often argued that it proves the second law of thermodynamics. A bit of judicious searching the internet will find all sorts of debunking of that claim and, indeed, it does not *quite* do such a thing. But it is weird that it is a topic, then, in so many statistical mechanics courses. Why this weird theorem that doesn't really have much practical application beyond its cute result? Well, one possible answer struck me when watching this video. This is the work that Planck identified as being the first invocation of the logarithm in relation to statistical mechanical properties. So it is an homage to primacy rather than anything truly fundamental.

This is why I like this channel. In my physics education, I was taught superficial anecdotes about a lot of this history which gave almost hagiographic accounts of discovery and scientific advancement. Kathy approaches the subject from a much more contextual approach that uncovers some of the weirdness and arbitrariness that still infects our choice for approaching physics to this day. Thank you for this channel!

[tariqjadoon]

Explaining the history just makes learning about science so interesting. Awesome!

[wim]

Your work should be on the freshmen curriculum for every STEM course! I was lucky to have a physics and an optical physics instructor much like this, starting from the basics and open our eyes.

[BrightBlueJim]

I find myself becoming deeply absorbed in your articles, with an ever-increasing enthusiasm.

Keep it up - you are a gem.

[dougieh]

Love Boltzmann ❤️❤️❤️
I’ve been obsessed with Thermodynamics for sometime now. It’s both fascinating and disturbing. Can’t get enough!!!

RIP Ludwig!!!
The world wasn’t ready for you in your time but your ideas are common knowledge now.

More Thermodynamics pretty please. ❤️

[sherafgankhan]

Madam you are awesome. Ive been out of university since 1999, working as an electrical engineer now. Your videos make me go back in time and question what i have learned. In a good way! Thank you for your videos...

[enricolucarelli]

Wow! From Spain, all my respect and gratitude. I always thought that the historical development of knowledge is an essential ingredient towards its comprehension. Your videos are amazing 👏👏👏👏

[ogbanugot]

This was so good. Please do Bohr's model and then Planck. But I'll probably watch all four if you do them.

[aletheia]

Wow! I've just discovered this channel. Amazing piece of history. Amazing piece of work by Kathy. I think it is important to understand the historical context of physics, which is often disregarded, as we pursue of the fundamental laws of nature.

[artdonovandesign]

That was an incredible and mesmerizing video! Thank you, Prof. and... What is that beautiful painting on the wall?

[bobvar]

This was pretty awesome! Great history here. I always thought Boltzmann came up with it. My respect for Planck grows even further.

[bobbymcgeorge]

Ooooh Kathy, you are spoiling us! Another fantastic entropy video - many thanks!

[Trp]

The real joy you bring is not dependent on anything you say… you are electricity…
I enjoy so much your grasp of truth

[mapifisher]

Thanks so much for this awesome history! Didn't know how spoiled I was when you were putting out videos regularly.

[jakelabete]

Your 'lectures' are absolutely delightful.