Statistical Physics¶

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.
• A Large number of bodies means a lot of degrees of freedom (DoFs). The system is large if it is consisting of 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.

How 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 particle. 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. 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.

Vocabulary¶

Thermodynamics¶

Equilibrium System¶

Nonequilibrium System¶

Some Topics in Statistical Mechanics¶

Acknowledgement¶

In 2014, I took the statistical physics course at UNM. It was an 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 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.

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.

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

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

Read online: Statistical Physics Notes .