Introduction

Summary

  • Thermodynamics is a phenomenological theory – it is based on experimental observations.

  • In addition, thermodynamics is an effective theory of the microscopic theory. The microscopic theory could describe a solid-state system, classical liquid, quantum liquids, black holes, neutron stars, etc. . Statistical mechanics provides a framework to justify this effective theory.

  • Statistical mechanics has a broader impact than thermodynamics. Statistical mechanics studies emergent behavior when the number of degrees of freedom is large. It is naturally connected with information theory, dynamical systems, and complexity theory which might not have a direct relation to thermodynamics.

  • Reading materials:

    1. [Cal98]: Chapter 21 is a very interesting approach to discuss the symmetry and the conceptual foundation of thermostatistics.

    2. [Fer12]: A very concise introduction of thermostatistics.

    3. [Wol23]: How complexity emerges? What is the second law of thermodynamics from the computational point of view.

A little bit of history of me learning thermodynamics and statistical mechanics

When I was an undergraduate student, it was very challenging for me to understand thermodynamics. To some extent, I can follow the equations. However, it is difficult for me to make physical sense out of it. Luckily, the undergrad textbook we use is Thermal Physics by C. Kittel and Herbert Kroemer. The book contains some of the principles of statistical mechanics. The concepts related to statistical mechanics somehow make lots of sense to me. I felt I could understand what’s going on from the statistical physics point of view, and thermodynamics seems like a very different beast that I have no way to understand. So I just did the homework, prepared for the exams, and passed the course without really thinking about the logical structure between the two subjects. After that, I tried to explore other subjects, and I kept my confusion about thermodynamics in my “unsolved” question book for the future me.

I found it is okay to keep an “unsolved” question book during my research journey. The “unsolved” questions will keep coming back at you with different forms to force you to relearn them. My experience is that as long as one keeps an open mind and is honest with oneself, the re-education process is usually very fruitful. Now, I am teaching thermodynamics and statistical mechanics, which forces me to learn the subject again with a crew of fresh minds. I believe it will be a fun journey for all of us.

Course motivation

I will introduce the course from three angles in the following sections:

  1. The thermodynamics as an effective theory: how to understand thermodynamics from the conceptual point of view?

  2. The motivation: why learn statistical mechanics?

  3. The applications of statistical mechanics: what can statistical mechanics do for us?

Then, I will provide a road map for the course to have a rough picture of what we will learn in the next 18 weeks.