From classical statistical physics to quantum physics

In summary, Bolztmann introduced the Plank's constant and the indistinguishability of atoms/molecules, while Gibbs introduced the density operator and quantum statistical mechanics.
  • #1
Mishra
55
1
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.
 
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  • #2
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
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
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.
 
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  • #5
My German is even worse than my English but I'll try to look in that direction ;)
Thank you
 

1. What is the difference between classical statistical physics and quantum physics?

Classical statistical physics deals with the behavior of large systems of particles, where the individual particles are described by classical mechanics. Quantum physics, on the other hand, deals with the behavior of particles at the microscopic level using the principles of quantum mechanics.

2. How did classical statistical physics lead to the development of quantum physics?

The principles of classical statistical physics, such as the law of large numbers and the concept of statistical ensembles, provided a framework for understanding the behavior of large systems of particles. These principles were then applied to the microscopic level, leading to the development of quantum mechanics and quantum statistical mechanics.

3. What are some key concepts in classical statistical physics that are also applicable in quantum physics?

Some key concepts in classical statistical physics, such as entropy, temperature, and energy, are also applicable in quantum physics. However, their definitions and interpretations differ in the two theories due to the fundamental differences in their underlying principles.

4. Can classical statistical physics be used to accurately describe quantum systems?

No, classical statistical physics cannot accurately describe quantum systems. This is because quantum systems exhibit behaviors that are not observed at the classical level, such as wave-particle duality and quantum entanglement. Therefore, classical statistical physics is limited in its ability to describe and predict the behavior of quantum systems.

5. What are some current research topics related to the connection between classical statistical physics and quantum physics?

Some current research topics include studying the thermodynamics of quantum systems, developing quantum statistical mechanics, and exploring the relationship between classical chaos and quantum mechanics. Additionally, there is ongoing research on the application of classical statistical physics techniques, such as Monte Carlo simulations, to solve quantum mechanical problems.

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