  A surrogate data analysis is presented, which is based on the fluctuations of
the ``entropy'' $S$ defined in the natural time-domain [Phys. Rev. E {\bf 68},
031106, 2003]. This entropy is not a static one as, for example, the Shannon
entropy. The analysis is applied to three types of time-series, i.e., seismic
electric signals, ``artificial'' noises and electrocardiograms, and
``recognizes'' the non-Markovianity in all these signals. Furthermore, it
differentiates the electrocardiograms of healthy humans from those of the
sudden cardiac death ones. If $\delta S$ and $\delta S_{shuf}$ denote the
standard deviation when calculating the entropy by means of a time-window
sweeping through the original data and the ``shuffled'' (randomized) data,
respectively, it seems that the ratio $\delta S_{shuf}/\delta S$ plays a
key-role. The physical meaning of $\delta S_{shuf}$ is investigated.
