# Transformations

Equivalence of thermodynamic ensembles through Laplace and Legendre transforms.

Edit and compile if you like:

% equivalence of thermodynamic ensembles through Laplace and Legendre transforms

\documentclass[tikz]{standalone}

\usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture}[trafo/.style={midway,font=\tiny}]

\def\hd{2}\def\vd{0.5}

\node (Zm) at (0,0) {$Z_m(E)$};
\node[right=\hd of Zm] (Zc) {$Z_c(\beta)$};
\node[right=\hd of Zc] (Zg) {$Z_g(\mu)$};

\node[below=\vd of Zm] (Sm) {$\sigma = \frac{S_m}{N}$};
\node[below=\vd of Zc] (F) {$f = \frac{F}{N}$};
\node[below=\vd of Zg] (O) {$\frac{\Omega}{V}$};

\draw[->] (Zm) -- (Sm);
\draw[->] (Zc) -- (F);
\draw[->] (Zg) -- (O);

\draw[->] (Zm) -- (Zc) node[trafo,below] {Laplace in $E$};
\draw[->] (Zc) -- (Zg) node[trafo,below] {Laplace in $N$};

\draw[->] (Sm) -- (F) node[trafo,above] {Legendre in $\epsilon = \frac{E}{N}$};
\draw[->] (F) -- (O) node[trafo,above] {Legendre in $\rho = \frac{N}{V}$};

\end{tikzpicture}
\end{document}


Click to download: transformations.tex
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This file is available on tikz.netlify.app and on GitHub and is MIT licensed.
See more on the author page of Janosh Riebesell..