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methods. |
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|
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Although the two techniques employed seem dissimilar, they are both |
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< |
linked by the overarching principles of Statistical |
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> |
linked by the over-arching principles of Statistical |
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Mechanics. Statistical Mechanics governs the behavior of |
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both classes of simulations and dictates what each method can and |
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cannot do. When investigating a system, one must first analyze what |
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be configured to give $E_{\gamma}$. Further, if $\gamma$ is a subset |
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of a larger system, $\boldsymbol{\Lambda}\{E_1,E_2,\ldots |
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E_{\gamma},\ldots E_n\}$, the total degeneracy of the system can be |
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expressed as, |
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expressed as |
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\begin{equation} |
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\Omega(\boldsymbol{\Lambda}) = \Omega(E_1) \times \Omega(E_2) \times \ldots |
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\Omega(E_{\gamma}) \times \ldots \Omega(E_n) |
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\Omega(E_{\gamma}) \times \ldots \Omega(E_n). |
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\label{introEq:SM0.1} |
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\end{equation} |
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This multiplicative combination of degeneracies is illustrated in |
