statistical-mechanics
Installation
SKILL.md
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