# Statistical Mechanics¶

Lecture notes for stat mech.

# Acknowledgement¶

I have finished the whole set of notes for my statistical mechanics class which is taught by V. M. Kenkre 2014 Spring.

Professor Kenkre’s lectures are as fantastic as an excellent thrilling movie without which I could never finish notes like this. I am very grateful to him for this adventure to modern statistical mechanics. The words I can think of to describe these lectures are the words used on the best chinese novel, Dream of the Red Chamber:

which is too hard to translate. It basically means that the subplot permeats through thousands of pages before people realize it’s importance. Professor Kenkre’s lectures do have such power that a tiny hint could develop into an important result as the lectures go on.

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 central topic of physics. It taught us great lessons about nature and it is definitely going to teach us more. Some ideas (Verlinde’s scenario) even put thermodynamics and statistical physics as the fundamental of all theories thus the thought that everything is emergent has been announced.

Basically, statistical mechanics is the mechanics of large bodies.

• Mechanics is Newton’s plan of kinematics.
• Large means a lot of DoFs. Usually DoFs add up to $$10^{23}$$ which is the order of Avogadro’s number.
• Bodies, of course, is the subject or system we are dealing with.

One question worth thinking about is how we end up with probabilities.

We wouldn’t need probability theory if we carry out Newton’s plan exactly. Note that the first thing we drop to come over the obstacles is to drop initial condition because it’s impossible to write down the initial condition of a large system for each particle. The price of that is we have to use probability to describe the system. Later on we find out that some dynamics have to be dropped to make it calculable which then gives us other sources of probability.

It’s kind of disappointing that stat mech is so vague.

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