Knowra Canonical ensemble Canonical ensemble A statistical-mechanical ensemble for systems in thermal equilibrium with a heat reservoir, at fixed temperature, volume, and particle number. Its probability weights are set by the Boltzmann factor.
Boltzmann distribution : A probability distribution that assigns states weights proportional to the exponential of negative energy divided by thermal energy. It gives each accessible microstate its canonical probability weight.
Microstate : A complete specification of the microscopic state of a physical system. Canonical probabilities are assigned to these individual states.
Microcanonical ensemble : An ensemble of isolated systems with fixed energy, volume, and particle number. Unlike the canonical ensemble, it fixes energy rather than temperature.
Canonical partition function of the harmonic oscillator : The partition function for a quantum oscillator in thermal equilibrium, summed over its equally spaced energy levels. It provides an exact model for seeing temperature-dependent occupation of energy levels.
Partition function : A sum or integral of statistical weights that normalizes probabilities and generates thermodynamic quantities. It normalizes the ensemble and encodes its equilibrium thermodynamics.
Energy level : An allowed value of a system's energy, often associated with one or more quantum states. The energy of each state controls its Boltzmann weight.
Grand canonical ensemble : An ensemble for systems exchanging both energy and particles with reservoirs, at fixed temperature, volume, and chemical potential. It relaxes the fixed-particle-number constraint and allows particle exchange.
Two-state system : A system with two allowed states, often used to model thermal occupation and magnetic moments. Its canonical probabilities give a simple example of thermal population changes.
Helmholtz free energy : A thermodynamic potential equal to internal energy minus temperature times entropy, natural at fixed temperature and volume. The canonical partition function determines this ensemble's central thermodynamic potential.
Temperature : A thermodynamic state variable that characterizes thermal equilibrium and sets the direction of heat flow. It sets the scale governing how strongly energy differences affect probabilities.
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