Statistical Physics & Thermodynamics From Beginner To Expert

Understand the theoretical physics of statistical mechanics (classical and quantum level) and apply it to thermodynamics

What you'll learn
Basics: Tutorial of classical mechanics and statistics
Theory: Statistical physics of isolated, closed & open systems
Application: Thermodynamics with many examples
Advanced project: Phase transitions based on statistical physics and Monte Carlo algorithms
Requirements
Basics about derivatives and integrals (College level)
For everything else there will be a whole tutorial section
Description
This course is for everyone who wants to learn about statistical physics!A bit of college mathematics (basic derivatives) is all you need to know!Understanding the motion of a single object is possible using the laws of classical mechanics. However, when we want to consider billions of particles at the same time, we need a new method: Statistical physics. The theory behind this approach is fascinating due to its simplicity. Still, it allows to correctly predict the laws of thermodynamics.You are kindly invited to join this carefully prepared course in which we derive the following concepts from scratch. I will present examples and have prepared quizzes and exercises for all topics.Optional tutorial of the essential basics (2 hours)Laws of classical mechanicsStatistics & stochasticsTheory of statistical physics (3 hours)Isolated, closed and open systems (micro canonical, canonical and grand canonical ensembles)Probability density, partition function and average valuesApplications and examples (6 hours)Entropy, temperature and the laws of thermodynamics Thermodynamic properties of gases Phase transitionsAt the end of the course there is even an optional section in which we simulate a phase transition using python. This is state of the art research!Why me?My name is Börge Göbel  and I am a postdoc working as a scientist on theoretical magnetism. Therefore, I use statistical physics very often but I have not forgotten the time when I learned about this theory and still remember the problems that I and other students had. I have refined my advisor skills as a tutor of Bachelor, Master and PhD students in theoretical physics and have other successful courses here on Udemy.I hope you are excited and I kindly welcome you to our course!

Overview

Section 1: Introduction & Physical background

Lecture 1 Overview of the course

Lecture 2 Classical mechanics background

Lecture 3 Newton's laws of motion

Lecture 4 Energy conservation law

Lecture 5 Hamiltonian mechanics

Lecture 6 What about statistical physics?

Lecture 7 Section summary

Lecture 8 Download the structure of this course

Lecture 9 Slides of this section

Section 2: [Optional] Mathematical background: Stochastics

Lecture 10 Section intro

Lecture 11 Probability & Tree diagrams for coin flip experiments

Lecture 12 Event & Counter event in a dice experiment

Lecture 13 Expectation values for coin, dice & urn problems

Lecture 14 Calculating probabilities: Urn problems

Lecture 15 Binomial distribution

Lecture 16 Discussion of the binomial distribution

Lecture 17 Normal distribution (Gaussian distribution)

Lecture 18 Poisson distribution

Lecture 19 Section outro

Lecture 20 [Exercises] Stochastics

Lecture 21 [Solution] Task 1 - Probabilities

Lecture 22 [Solution] Task 2 - Probabilities

Lecture 23 [Solution] Task 3 - Probabilities

Lecture 24 Slides of this section

Section 3: From microstates to the partition function of canonical ensembles

Lecture 25 Section intro

Lecture 26 Microstates

Lecture 27 Microstates versus macrostates

Lecture 28 Example: Statistical treatment of the harmonic oscillator

Lecture 29 Microcanonical ensemble

Lecture 30 Canonical ensemble

Lecture 31 Probability of the canonical ensemble

Lecture 32 Partition function

Lecture 33 Example: Kinetic energy of a gas - Definition of the temperature

Lecture 34 Example: Kinetic energy of a gas - Maxwell velocity distribution

Lecture 35 [Exercise] Barometric height formula

Lecture 36 [Solution] Potential energy of a gas - Barometric formula

Lecture 37 Equivalence of canonical and microcanonical ensemble in the thermodynamic limit

Lecture 38 Summary: Canonical and microcanonical ensembles

Lecture 39 Section outro

Lecture 40 Quantum statistics example: Quantum harmonic oscillator

Lecture 41 Optional: Liouville equation

Lecture 42 Slides of this section

Section 4: Laws of thermodynamics & Thermodynamic potentials

Lecture 43 Section intro

Lecture 44 First law of thermodynamics

Lecture 45 Thermodynamic Work

Lecture 46 Pressure

Lecture 47 Second law of thermodynamics

Lecture 48 Entropy

Lecture 49 Third law of thermodynamics

Lecture 50 [Exercise] Entropy of a die

Lecture 51 [Solution] Entropy of a die

Lecture 52 Entropy of a black hole

Lecture 53 Internal energy U as a thermodynamic potential

Lecture 54 Helmholtz free energy F

Lecture 55 Enthalpy H

Lecture 56 Gibbs free energy G

Lecture 57 Maxwell relations

Lecture 58 Section summary: Thermodynamic square

Lecture 59 Slides of this section

Section 5: Thermodynamics of gases

Lecture 60 Section intro

Lecture 61 Ideal gas

Lecture 62 Thermodynamic processes

Lecture 63 Isentropic processes

Lecture 64 Heat capacity

Lecture 65 Compressibility

Lecture 66 Thermal expansion

Lecture 67 Application: Thermodynamic cycles

Lecture 68 Efficiency of thermodynamic cycles

Lecture 69 Carnot cycle

Lecture 70 Real gas

Lecture 71 Slides of this section

Lecture 72 Section outro

Section 6: Phase transitions in Landau theory

Lecture 73 Section intro

Lecture 74 Phase transitions

Lecture 75 Landau theory

Lecture 76 Example: 2nd-order phase transition in Landau theory

Lecture 77 Example: 1st-order phase transition in Landau theory

Lecture 78 Slides of this section

Lecture 79 Section outro

Section 7: Grand canonical ensemble: Open systems with variable number of particles

Lecture 80 Section intro

Lecture 81 Partition function of the grand (macro) canonical ensemble

Lecture 82 Grand canonical potential & Entropy

Lecture 83 Non-interacting quantum gas

Lecture 84 Quantum statistics: Bosons versus fermions

Lecture 85 Fermions: Fermi-Dirac statistics

Lecture 86 Bosons: Bose-Einstein statistics

Lecture 87 Bose-Einstein condensate: Behavior at low temperature

Lecture 88 Transition to the classical Maxwell-Boltzmann distribution function

Lecture 89 Slides of this section

Lecture 90 Section summary

Section 8: [Advanced Project] Magnetism I: Statistical Physics

Lecture 91 Section intro

Lecture 92 Zeeman energy

Lecture 93 Ising model

Lecture 94 Partition function of a paramagnet

Lecture 95 Magnetization of a paramagnet

Lecture 96 Heisenberg interaction

Lecture 97 Ferromagnet in mean-field approximation

Lecture 98 Phase transition: Ferromagnet versus paramagnet

Section 9: [Advanced Project] Magnetism II: Monte Carlo Algorithm

Lecture 99 Section intro

Lecture 100 Installing Python and Jupyter Notebook

Lecture 101 About Monte Carlo algorithms

Lecture 102 Python template Part 1: Approximating Pi

Lecture 103 Calculating Pi - Explaining the idea behind the algorithm

Lecture 104 Approximating Pi

Lecture 105 Alternative solution and time comparison for approximating Pi

Lecture 106 Python template Part 2: Simulating a magnet

Lecture 107 Magnetism: Setting up & plotting the initial state

Lecture 108 Defining the energy

Lecture 109 Simulating a Metropolis step

Lecture 110 Running the Monte Carlo algorithm

Lecture 111 Adding finite temperatures

Lecture 112 Implement interaction with a magnetic field

Lecture 113 Dzyaloshinskii–Moriya interaction

Lecture 114 Python template Part 3: Temperature and field dependence of the magnetization

Lecture 115 Clean up the code and use functions

Lecture 116 Magnetization versus temperature

Lecture 117 Magnetization versus magnetic field

Lecture 118 Magnetization versus magnetic field in a paramagnet

Lecture 119 Thank you & Goodbye!

Students in science & engineering,Everyone who knows about classical mechanics and wonders what comes next