% miko:type: atomic
% miko:title: Microcanonical Ensemble
% miko:summary: The equal-probability ensemble for isolated systems at fixed energy.
% miko:tags: statmech
% miko:difficulty: undergrad
% miko:related: complete-statistical-mechanics, boltzmann-distribution, entropy-second-law
% miko:keywords: isolated system, entropy, phase space

\documentclass{article}
\usepackage{amsmath}
\title{Microcanonical Ensemble}
\begin{document}
\maketitle

\section{Fixed Energy}

The microcanonical ensemble describes an isolated system with fixed $E,V,N$.
Allowed microstates compatible with the macroscopic constraints are assigned
equal probability.

\section{Entropy}

If $\Omega(E,V,N)$ is the number of accessible states, the entropy is

$$
S=k_B\ln\Omega.
$$

Temperature is then defined by

$$
\frac{1}{T}=\left(\frac{\partial S}{\partial E}\right)_{V,N}.
$$

\end{document}
