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Canonical ensemble
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System in contact with a heat bath.
A system in contact with a heat bath at fixed T, exchanging energy but not particles, follows the Boltzmann distribution. Energy fluctuates around the mean.
A beaker of water in a room.
Fluctuations are tiny for macroscopic systems.
In more detail
In a canonical ensemble, a system is in contact with a heat bath at fixed temperature. Its probabilities follow the Boltzmann distribution, which makes calculations of thermodynamic properties straightforward.
Real-world uses
- Computer simulations of molecular systems often use the canonical ensemble.
- Physical chemistry describes solutions and solids this way.
- Chemists model a molecule in a solvent as a system in contact with a heat bath, which is described by the canonical ensemble.
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Frequently asked questions
How does it differ from the microcanonical ensemble?
The canonical ensemble has fixed temperature, while the microcanonical has fixed energy.
Why use an ensemble?
It replaces a single system with a statistical description that is easier to handle.
What is the difference from a microcanonical ensemble?
The canonical ensemble allows energy to flow with a heat bath at fixed temperature, while the microcanonical ensemble has fixed energy.
Related topics in Kinetic Theory & Statistical Physics
Microstates and macrostates · Boltzmann distribution · Partition function · Fermi–Dirac statistics · Bose–Einstein statistics · Bose–Einstein condensate