Partition Function
Definition
The master key of statistical mechanics — one sum over all possible states that unlocks energy, entropy, everything.
Symbol: ·
Technical definition
Z = Σ e^(−Eᵢ/kT). All thermodynamics follows: F = −kT ln Z, and state probabilities are pᵢ = e^(−Eᵢ/kT)/Z (the Boltzmann distribution).
Example
For a two-level system (like a coin that costs energy ε to flip heads), Z = 1 + e^(−ε/kT) predicts the exact fraction of heads at any temperature.
Common confusion
The partition function is not itself a probability — it is the normalization sum. Each state's probability is its term divided by Z.