  There is a growing interest in methods for detecting and interpreting changes
in experimental time evolution data. Based on measured time series, the
quantitative characterization of dynamical phase transitions at bifurcation
points of the underlying chaotic systems is a notoriously difficult task.
Building on prior theoretical studies that focus on the discontinuities at
$q=1$ in the order-$q$ R\'enyi-entropy of the trajectory space, we measure the
derivative of the spectrum. We derive within the general context of Markov
processes a computationally efficient closed-form expression for this measure.
We investigate its properties through well-known dynamical systems exploring
its scope and limitations. The proposed mathematical instrument can serve as a
predictor of dynamical phase transitions in time series.
