Statistical Physics

This started as a set of lecture notes for the statistical physics course I took. Then I expanded it and rebuilt it into something much more useful.

Acknowledgement

In 2014, I took the statistical physics course at UNM. It was a one early morning course taught by Professor V. M. Kenkre. I was never a fan of morning classes but this statmech course was one of the best courses I have ever took.

Professor Kenkre’s lectures are fantastic. He made the lectures to be as inspiring and exciting as thrilling movies. Professor Kenkre’s lectures have such a power that a tiny hint would develop into an important result as the adventure goes on. The only words I can think of for the lectures are the words used on the best chinese novel, Dream of the Red Chamber.

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It says that the subplot permeates through thousands of pages before people realize it’s importance.

I am very grateful to him for this adventure of modern statistical mechanics. I am also very grateful to the TA of this course, Anastasia, who helped me a lot with my homework and lecture notes.

Introduction

Statistical Physics is the holy grail of physics. It taught us great lessons about this universe and it is definitely going to teach us more. Some ideas (such as Verlinde’s scenario) even put thermodynamics and statistical physics as the fundamental theory of all theories. This leads to the thought that it is possible that everything is a result of emergence.

Statistical mechanics is the mechanics of large bodies.

  • Classical Mechanics is Newton’s plan of kinematics.

  • Large number of bodies means a lot of degrees of freedom (DoFs). The system is large if the DoFs add up to \(10^{23}\). That being said, we would study matter consisting Avogadro’s number of particles.

  • Bodies, as mentioned above, is the subject or system that we are dealing with.

One interesting question about statistical mechanics is how we ended up with probabilities.

We wouldn’t need probability theory if we carry out Newton’s plan exactly, in theory. But we do not have such computing powers. So we give up something for computability. The first thing we compromise is to drop the initial conditions of the particles. The reason is that it’s impossible to write down all the initial conditions of all the particles. Then we find that we can’t track the trajectory of all the particles so we anonymize them. In order to describe these anonymized particles, we have to use probability. What’s more, some detailed dynamics of the particles have to be dropped to make our statistical quantities calculable. This is another reason that we turn to probabilities.

Though it’s kind of disappointing that Newton’s plan didn’t succeed, this conflict between Newton’s plan and our nature brought us new insights about our world.

Some Topics in Statistical Mechanics


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This open source project is hosted on GitHub: Statistical Physics .

Read online: Statistical Physics Notes .

Download the Latest PDF Version .


Many thanks to open source project Sphinx for it saves me a lot of time on making this website.


The sitemap of the website can be downloaded from: sitemap.xml or sitemap.xml.gz .


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