More dimensions—Less entropy

For a cosmological model with $d$ noncompact and $D$ compact spatial dimensions and symmetry $R^1\times S^d\times S^D$, we calculate the entropy produced in $d$ dimensions due to the compactification of $D$ dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions.