Newton's laws of motion

Classical mechanics background

Energy conservation law

Overview of the course

Hamiltonian mechanics

What about statistical physics

Section summary

Section intro

Probability & Tree diagrams for coin flip experiments

Event & Counter event in a dice experiment

Expectation values for coin, dice & urn problems

Calculating probabilities Urn problems

Binomial distribution

Discussion of the binomial distribution

Normal distribution (Gaussian distribution)

Poisson distribution

Section outro

[Solution] Task 1 - Probabilities

[Solution] Task 2 - Probabilities

[Solution] Task 3 - Probabilities

Microstates versus macrostates

Example Statistical treatment of the harmonic oscillator

Canonical ensemble

Microcanonical ensemble

Probability of the canonical ensemble

Partition function

Example Kinetic energy of a gas - Definition of the temperature

Example Kinetic energy of a gas - Maxwell velocity distribution

[Solution] Potential energy of a gas - Barometric formula

Equivalence of canonical and microcanonical ensemble in the thermodynamic limit

Summary Canonical and microcanonical ensembles

Section outro

Quantum statistics example Quantum harmonic oscillator

Optional Liouville equation

First law of thermodynamics

Thermodynamic Work

Second law of thermodynamics

Pressure

Entropy

Third law of thermodynamics

[Exercise] Entropy of a die

[Solution] Entropy of a die

Internal energy U as a thermodynamic potential

Enthalpy H

Helmholtz free energy F

Gibbs free energy G

Maxwell relations

Section summary Thermodynamic square

Ideal gas

Thermodynamic processes

Heat capacity

Isentropic processes

Compressibility

Thermal expansion

Efficiency of thermodynamic cycles

Application Thermodynamic cycles

Carnot cycle

Real gas

Section outro

Phase transitions

Landau theory

Example 2nd-order phase transition in Landau theory

Example 1st-order phase transition in Landau theory

Section outro

Partition function of the grand (macro) canonical ensemble

Grand canonical potential & Entropy

Non-interacting quantum gas

Fermions Fermi-Dirac statistics

Quantum statistics Bosons versus fermions

Bosons Bose-Einstein statistics

Bose-Einstein condensate Behavior at low temperature

Transition to the classical Maxwell-Boltzmann distribution function

Section summary

Zeeman energy

Ising model

Heisenberg interaction

Partition function of a paramagnet

Magnetization of a paramagnet

Ferromagnet in mean-field approximation

Phase transition Ferromagnet versus paramagnet

Installing Python and Jupyter Notebook

About Monte Carlo algorithms

Calculating Pi - Explaining the idea behind the algorithm

Alternative solution and time comparison for approximating Pi

Approximating Pi

Defining the energy

Magnetism Setting up & plotting the initial state

Running the Monte Carlo algorithm

Simulating a Metropolis step

Adding finite temperatures

Implement interaction with a magnetic field

Clean up the code and use functions

Dzyaloshinskii–Moriya interaction

Magnetization versus temperature

Thank you & Goodbye!

Magnetization versus magnetic field

Magnetization versus magnetic field in a paramagnet