Examples of devices where phonon noise is important include bolometers and calorimeters.
Johnson–Nyquist noise is easily modeled at thermal equilibrium, where all components of the circuit are held at the same temperature.
A general equilibrium model for phonon noise is usually impossible because different components of the thermal circuit are nonuniform in temperature and also often not time invariant, as in the occasional energy deposition from particles incident on a detector.
The transition edge sensor typically maintains the temperature through negative electrothermal feedback associated with changes in internal electrical power.
due to phonon noise near quasi-equilibrium is described using a similar formula, where C is the heat capacity.
[3] A real bolometer or calorimeter is not at equilibrium because of a temperature gradient between the absorber and the bath.