 Temperature fluctuation

A temperature fluctuation is a varying departure $\delta T$ from a specified mean temperature. Its meaning depends on the subsystem, averaging time and measurement procedure. Even in thermal equilibrium, a finite body exchanging energy with a reservoir has energy fluctuations. The reservoir temperature parameter can remain fixed while the body's energy changes.

For a small departure from local equilibrium, an energy-based temperature estimate obeys $\delta T\simeq \delta E/C_V$. Combining this linear relation with the canonical energy fluctuation givesThis estimate uses positive heat capacity and small relative fluctuations; it is not a universal definition of an instantaneous microscopic temperature. Larger heat capacity suppresses these inferred variations. A thermometer's own electrical noise and finite response time can add or filter fluctuations, so observed signal variance must be separated from the thermal quantity one intends to measure.