# From classical statistical physics to quantum physics

1. Jan 17, 2015

### Mishra

Hello,

This is more a question about history of science in general.

During my lectures on statistical physics, I noticed that some of the problems that Bolztmann faced lead to the introduction of:
$h/2\pi$ (to introduce the unit of an action leading to a "unitless" partition function) which is nothing than the Plank's constant and the indistinguishability of atoms/molecules in a gaz introduced by Gibbs (in order to solve the Gibbs paradox).

Also, introducing the density operator, leading to quantum statistical mechanics is very simple, smooth and elegant.

Is it safe to say that the Boltzmann theory of gaz was be the first to introduce fundamental notions of quantum physics (the quanta, and the indistinguishability)? If so, do we know if these were helpful and used during the construction of quantum physics ? Is there anything to read about it (could not find anything yet) ?

Thank you and have a great day.

2. Jan 17, 2015

### dextercioby

I think the so-called <cellulation> of phase space in quanta of h is also due to Gibbs. The Boltzmann's theory of gases has its merits, but not related to quantum physics. With all due respect for the great Austrian, he was non-productive in Physics in the last years of his life, which coincided with the early development of the quantization ideas.

3. Jan 17, 2015

### Mishra

I knew I did'nt have anything to do with the quantization, I read he was deeply depressed and incapacitated during his later years.
But I was asking if the work of Gibbs to "fix" the statistical mechanics (hbar and indistinguishability) gave inspiration to the fathers of quantum physics. Or did we realized later that those properties of matter were already encoded in statistical mechanics and were, in fact, not that new ?

4. Jan 17, 2015

### dextercioby

I cannot assess the influence of Gibbs upon the founders of Quantum Mechanics (1925-). Bose for instance mentions the cellulation of classical phase space in his famous article here: http://link.springer.com/article/10.1007/BF01327326 but he didn't mention Gibbs at all.

Last edited: Jan 17, 2015
5. Jan 20, 2015

### Mishra

My German is even worse than my English but I'll try to look in that direction ;)
Thank you