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 early-morning course taught by Professor V. M. Kenkre. I was never a fan of early-morning classes but Professor Kenkre’s statmech lectures were among the best lectures I have ever took.

Professor Kenkre’s lectures are truly fantastic. He made the lectures to be as inspiring and exciting as thrilling movies. Those lectures had 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 to describe them 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 definitely will teach us more. Some ideas (such as Verlinde’s scenario) even place thermodynamics and statistical physics as the fundamental theory of all theories. This leads to the thought that it might be possible that everything is a result of emergence.

Statistical mechanics is the mechanics of large bodies using statistical methods.

  • Classical mechanics is Newton’s great plan of kinematics.

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

  • Each member of the system is responsible for the properties of the whole system but we can’t explain everything using the single particle properties. More is different.

Wow did we end up with probabilities?

We wouldn’t need statistics if we could carry out Newton’s plan exactly, in theory. But we do not have such computing powers nor such detailed knowledge of each particle. So we give up the detailed kinematics of each particles. First things first, we drop the initial conditions of the particles. The argument is that it’s impossible to write down all the initial conditions of all the particles given the experimental technology and potato computers we have. Secondly, we can’t track the trajectory of all the particles so we anonymize them. In order to describe these anonymized particles, we use probabilities. What is even more intriguing is that some detailed dynamics of the particles have to be dropped to make our statistical quantities calculable. With these simplifications, statistics is then powerful enough to predict many physical observables.

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

Equilibrium System

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 .


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