% miko:type: atomic
% miko:title: Partition Function
% miko:summary: The statistical object from which thermodynamic quantities are derived.
% miko:tags: thermo
% miko:difficulty: undergrad
% miko:related: entropy-second-law, gibbs-free-energy, complete-thermodynamics
% miko:keywords: ensemble, Boltzmann weight, free energy

\documentclass{article}
\usepackage{amsmath}
\title{Partition Function}
\begin{document}
\maketitle

\section{Canonical Ensemble}

For states with energies $E_i$,

$$
Z = \sum_i e^{-\beta E_i},
\qquad \beta = \frac{1}{k_B T}.
$$

\section{Free Energy}

The Helmholtz free energy is

$$
F = -k_B T\ln Z.
$$

\end{document}
