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Partition function
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Sum over states from which all thermodynamic quantities follow.
Z = Σe^{−E/kT}Z = Σe^{−E_i/kT} sums over all states and provides all thermodynamic quantities: F = −kT ln Z, U = −∂ln Z/∂β.
Two-level system Z = 1 + e^{−ΔE/kT}.
Z normalises probabilities.
In more detail
The partition function Z sums exp(−E/kT) over all states, and it connects microscopic states to thermodynamic quantities such as energy, entropy and free energy.
Real-world uses
- Physicists compute thermodynamic properties of solids and gases from partition functions.
- Chemists use them to calculate equilibrium constants.
- Physicists calculate thermodynamic quantities from the partition function, which sums the contributions of all possible states.
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Frequently asked questions
What is the physical meaning?
It counts the effective number of accessible states at a given temperature.
Why is it powerful?
Once Z is known, many thermodynamic properties follow by differentiation.
Why is the partition function so useful?
Once you know it, you can derive energy, entropy and pressure, so it connects the microscopic and macroscopic descriptions.
Related topics in Kinetic Theory & Statistical Physics
Liquefaction of gases · Microstates and macrostates · Boltzmann distribution · Canonical ensemble · Fermi–Dirac statistics · Bose–Einstein statistics