The definition and measurement of the topological entropy per unit volume in parabolic PDEs

We define the topological entropy per unit volume in parabolic PDEs such as the complex Ginzburg-Landau equation, and show that it exists and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.