Helmholtz free energy (issue 103)

Author: davidlmobley

paper/basic_training.tex

@@ -304,7 +304,7 @@ \subsubsection{Key concepts}
 For a \emph{continuous} coordinate (e.g., the distance between two residues in a protein), the probability-determining free energy is called the ``potential of mean force'' (PMF); the Boltzmann factor of a PMF gives the relative probability of a given coordinate.
 Any kind of free energy implicitly includes \emph{entropic} effects; in terms of an energy landscape (Fig.\ \ref{landscapes}), the entropy describes the \emph{width} of a basin or the number of arrangements a system can have within a particular state.
 One way to think of this it is that entropy of a state relates to the \emph{volume} of 6N-dimensional phase space that the state occupies, which in the one-dimensional case is just the \emph{width}.
-These points are discussed in textbooks, as are the differences between free energies for different thermodynamic ensembles -- e.g., $F$, the Helmholtz free energy, when $T$ is constant, and $G$, the Gibbs free energy, when both $T$ and pressure are constant -- which are not essential to our introduction~\cite{DillBook, Zuckerman:2010:}.
+These points are discussed in textbooks, as are the differences between free energies for different thermodynamic ensembles -- e.g., $A$, the Helmholtz free energy, when $T$ is constant, and $G$, the Gibbs free energy, when both $T$ and pressure are constant -- which are not essential to our introduction~\cite{DillBook, Zuckerman:2010:}.\footnote{Occasionally $F$ is used to refer to either appropriate free energy, $A$ or $G$, but this is not standard.}
 
 A final essential topic is the difference between equilibrium and non-equilibrium systems.
 We noted above that an MD trajectory is not likely to represent the equilibrium ensemble because the trajectory is probably too short.