  This paper presents a new abstract method for proving lower bounds in
computational complexity. Based on the notion of topological and measurable
entropy for dynamical systems, it is shown to generalise three previous lower
bounds results from the literature in algebraic complexity. We use it to prove
that $\mathtt{maxflow}$, a $\mathrm{Ptime}$ complete problem, is not computable
in polylogarithmic time on parallel random access machines (prams) working with
real numbers. This improves on a result of Mulmuley since the class of machines
considered extends the class "prams without bit operations". We further improve
on this result by showing that euclidean division cannot be computable in
polylogarithmic time using division on the reals, pinpointing that euclidean
division provides a significant boost in expressive power.
  On top of showing this new separation result, we show our method captures
previous lower bounds results from the literature: Steele and Yao's lower
bounds for algebraic decision trees, Ben-Or's lower bounds for algebraic
computation trees, Cucker's proof that $\mathrm{NC}$ is not equal to
$\mathrm{Ptime}$ in the real case, and Mulmuley's lower bounds for prams
without bit operations.
