Thermal fluctuation
= Thermal fluctuation
{title2=$\langle(\delta A)^2\rangle=k_BT\,\partial_h\langle A\rangle$}
A thermal fluctuation is the randomness of an observable in an equilibrium <Boltzmann distribution>. If the energy contains $-hA$, differentiation of its <partition function> gives $\partial_h\langle A\rangle=\beta(\langle A^2\rangle-\langle A\rangle^2)$. Thus the fluctuation variance is related to the response to a conjugate source. In a field theory, the two-point version is the <connected correlation function>.