Abstract
An introduction to basic concepts from statistical and classical mechanics, as required to understand this thesis.
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Notes
- 1.
Here is a brief derivation of Eq. (3.12).
$$\begin{aligned} \Delta f_i \Delta f_j =&\left( f_i - \overline{f_i}\right) \left( f_j - \overline{f_j}\right) \\ =&f_i f_j - f_i \overline{f_j} - f_j \overline{f_i} +\overline{f_i}\,\overline{f_j} \\ \Rightarrow \overline{\Delta f_i \Delta f_j} =&\overline{f_i f_j} -\overline{f_i}\,\overline{f_j} \end{aligned}$$Since \(f_i\) and \(f_j\) are independent
$$\begin{aligned} \overline{f_i f_j} = \overline{f_i}\,\overline{f_j}. \end{aligned}$$Therefore we have
$$\begin{aligned} \overline{\Delta f_i \Delta f_j} = 0 \; : \; i \ne j . \end{aligned}$$
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Baldock, R.J.N. (2017). Introduction. In: Classical Statistical Mechanics with Nested Sampling. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-66769-0_3
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DOI: https://doi.org/10.1007/978-3-319-66769-0_3
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