The system is then mapped back onto the original area by cutting and restacking, which we can call a ‘fold’. The inverse transformation is accomplished by stretching first in the vertical (\(p\)) dire...The system is then mapped back onto the original area by cutting and restacking, which we can call a ‘fold’. The inverse transformation is accomplished by stretching first in the vertical (\(p\)) direction and squashing in the horizontal (\(q\)) direction, followed by a slicing and restacking.
Note that \(D(E)\) has dimensions of inverse energy, so one might ask how we are to take the logarithm of a dimensionful quantity in Equation \ref{statent}. We must introduce an energy scale, such as ...Note that \(D(E)\) has dimensions of inverse energy, so one might ask how we are to take the logarithm of a dimensionful quantity in Equation \ref{statent}. We must introduce an energy scale, such as \(\RDelta E\) in Equation \ref{DOSeqn}, and define \({\tilde D}(E;\RDelta E)=D(E)\,\RDelta E\) and \(S(E;\RDelta E)\equiv\kB\ln {\tilde D}(E;\RDelta E)\).