# Statistical Mechanics

> Statistical physics and thermodynamics

- Skill: `ffsshhttiikk/statistical-mechanics` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/statistical-mechanics`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/statistical-mechanics/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/statistical-mechanics

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## 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