= Temperature fluctuation
{title2=$\delta T=T-\overline T$}
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> gives
$$
\langle(\delta T)^2\rangle\simeq\frac{k_BT^2}{C_V}.
$$
This 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.
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