🎲 Introduction to Classical Statistical Mechanics

We learn the concepts of phase space and microstates, the principle of equal a priori probability, and the definition of the microcanonical ensemble. We derive Boltzmann's entropy formula and calculate the entropy and equation of state of an ideal gas using Python.

We learn the definition of the canonical ensemble, the canonical partition function, and Helmholtz free energy. We derive internal energy, entropy, and heat capacity from the partition function, and implement harmonic oscillator systems and the Einstein solid model using Python.

We learn the definition of the grand canonical ensemble, the grand partition function, and the concept of chemical potential. We derive the grand partition function for an ideal gas and implement adsorption isotherms (Langmuir adsorption) and the lattice gas model using Python.

We derive the Maxwell velocity distribution for classical ideal gases and learn the basics of quantum statistics (Fermi-Dirac distribution, Bose-Einstein distribution). We calculate the Planck distribution for photon gas and the density of states for Fermi electron systems using Python.

We learn the theory of the Ising model (mean-field approximation, critical phenomena) and implement the Metropolis Monte Carlo method algorithm. Through simulation of the 2D Ising model, we calculate phase transitions and critical exponents using Python.