Statistical thermodynamics in isolated systems - overview of statistics, probability of states, microstates vs. macrostates, entropy, most probable distribution
Systems at constant temperature - the Boltzmann distribution, partition function, thermodynamic variables from the partition function, fluctuations, thermodynamic ensembles - concepts, definitions, concepts and examples
Systems of non-interacting particles - single-particle partition function, monoatomic, diatomic and polyatomic ideal gas, Fermi-Dirac and Bose-Einstein statistics, ideal gas mixtures and chemical equilibria
Interacting systems - quantum-mechanical and classical statistical thermodynamics, configuration integral, configuration space and phase space, virial expansion in real gases
The Monte Carlo simulation method - sampling the configuration space, Metropolis algorithm, detailed balance, ergodicity, simple sampling and importance sampling, initialization, equilibration, sampling
Simulations of interacting particles - interaction potentials, computer model, periodic boundary conditions, examples of interaction potentials, theorem of corresponding states and reduced units, short-range vs. long-range interactions, computing ensemble averages and thermodynamic properties from the simulation, statistical analysis of correlated time series
The Ising model in 1D, 2D and 3D - phase transitions, coexistence, spontaneous symmetry breaking, ergodicity, the mean-field approach, MC simulation of the Ising model, single-particle trial moves and collective trial moves,
Statistical thermodynamics of the liquid state - pair correlation function, statistical theories of the liquid state - integral equations and perturbation theories
Molecular dynamics - sampling the phase space vs. sampling the configuration space, numerical integration of equations of motion, MD at constant temperature, computing thermodynamic variables and transport coefficients, Green-Kubo relations
Solutions of electrolytes and polyelectrolytes, Debye length and Bjerrum length, long-range interactions in simulations - Ewald summation and related techniques,
Biased sampling in Monte Carlo, simulations in the grandcanonical ensemble, isothermal-isobaric ensemble, reaction ensemble and constant pH ensemble
Thermodynamic integration for calculating free energies in simulations, Gibbs ensemble for simulating phase equilibria
(optional) Non-equilibrium statistical thermodynamics, and non-equilibrium simulations