attempt at entropy question

Author: samarjeet

paper/basic_training.pdf

@@ -302,7 +302,8 @@ \subsubsection{Key concepts}
 Because equilibrium behavior is caused by dynamics, there is a fundamental connection between rates and equilibrium, namely that $\peq_A k_{AB} = \peq_B k_{BA}$, which is a consequence of ``detailed balance''.
 There is a closely related connection for on- and off-rates with the binding equilibrium constant. 
 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 quantifies the \emph{width} of a basin.  
+Any kind of free energy implicitly includes \emph{entropic} effects; in terms of an energy landscape (Fig.\ \ref{landscapes}), the entropy quantifies the \emph{width} of a basin.
+One way to visualize it is that entropy of a state is 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:}.
 
 A final essential topic is the difference between equilibrium and non-equilibrium systems.