--- trunk/mattDisertation/Introduction.tex 2004/03/16 19:22:56 1091 +++ trunk/mattDisertation/Introduction.tex 2004/03/16 21:35:16 1092 @@ -21,7 +21,7 @@ linked by the overarching principles of Statistical methods. Although the two techniques employed seem dissimilar, they are both -linked by the overarching principles of Statistical +linked by the over-arching principles of Statistical Mechanics. Statistical Mechanics governs the behavior of both classes of simulations and dictates what each method can and cannot do. When investigating a system, one must first analyze what @@ -47,10 +47,10 @@ expressed as, be configured to give $E_{\gamma}$. Further, if $\gamma$ is a subset of a larger system, $\boldsymbol{\Lambda}\{E_1,E_2,\ldots E_{\gamma},\ldots E_n\}$, the total degeneracy of the system can be -expressed as, +expressed as \begin{equation} \Omega(\boldsymbol{\Lambda}) = \Omega(E_1) \times \Omega(E_2) \times \ldots - \Omega(E_{\gamma}) \times \ldots \Omega(E_n) + \Omega(E_{\gamma}) \times \ldots \Omega(E_n). \label{introEq:SM0.1} \end{equation} This multiplicative combination of degeneracies is illustrated in