Equations · equation
Partition Function
Statistical Mechanics · 1902
- Equation
- Z = Σᵢ e^(−Eᵢ/kT)
- Field
- Statistical Mechanics
- Named After
- Ludwig Boltzmann · Josiah Willard Gibbs
- Year
- 1902
Symbols
Z the sum over every state i the system can occupy · Eᵢ each state's energy · k Boltzmann constant · T absolute temperature · free energy follows as F = −kT·ln Z
Significance
One sum that knows everything: energy, entropy, pressure, heat capacity — every thermodynamic quantity is a derivative of ln Z. Statistical mechanics' entire program is 'compute Z, then differentiate', formalized in Gibbs' 1902 treatise.
Referenced by
constant
equation
theory
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