statistical-mechanics

## What I do - Apply statistical ensembles (microcanonical, canonical, grand canonical) - Calculate partition functions and thermodynamic quantities - Model ideal and real gases - Analyze phase transitions and critical phenomena - Study kinetic theory and transport phenomena - Apply the equipartition theorem ## When to use me When deriving thermodynamic properties from microscopic physics or studying collective phenomena. ## Key Concepts - **Partition Function**: Z = Σ_i e^{-βE_i} generates thermodynamic quantities - **Boltzmann Distribution**: P_i = e^{-βE_i}/Z for canonical ensemble - **Helmholtz Free Energy**: F = -k_BT ln Z relates to partition function - **Entropy**: S = k_B ln Ω (microcanonical), S = -k_B ΣP_i ln P_i (general) - **Equipartition Theorem**: Each quadratic degree contributes ½k_BT to energy - **Mean Free Path**: λ = 1/(√2nσ) for molecular collisions