% miko:type: atomic
% miko:title: Fluctuation-Response Relation
% miko:summary: Equilibrium fluctuations determine linear response coefficients.
% miko:tags: statmech
% miko:difficulty: graduate
% miko:related: canonical-ensemble, heat-capacity, ising-model
% miko:keywords: susceptibility, variance, response

\documentclass{article}
\usepackage{amsmath}
\title{Fluctuation-Response Relation}
\begin{document}
\maketitle

\section{Heat Capacity}

In the canonical ensemble, energy fluctuations determine the heat capacity:

$$
C_V=\frac{\langle E^2\rangle-\langle E\rangle^2}{k_BT^2}.
$$

\section{Susceptibility}

More generally, the response of an observable to a conjugate field is related
to the equilibrium variance of that observable. This is a central bridge
between microscopic fluctuations and macroscopic measurements.

\end{document}
