  We propose an information-theoretical measure, the \textit{relative cluster
entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among cluster partitions
characterised by probability distribution functions $P$ and $Q$. The measure is
illustrated with the clusters generated by pairs of fractional Brownian motions
with Hurst exponents $H_1$ and $H_2$ respectively. For subdiffusive, normal and
superdiffusive sequences, the relative entropy sensibly depends on the
difference between $H_1$ and $H_2$. By using the \textit{minimum relative
entropy} principle, cluster sequences characterized by different correlation
degrees are distinguished and the optimal Hurst exponent is selected. As a case
study, real-world cluster partitions of market price series are compared to
those obtained from fully uncorrelated sequences (simple Browniam motions)
assumed as a model. The \textit{minimum relative cluster entropy} yields
optimal Hurst exponents $H_1=0.55$, $H_1=0.57$, and $H_1=0.63$ respectively for
the prices of DJIA, S\&P500, NASDAQ: a clear indication of non-markovianity.
Finally, we derive the analytical expression of the relative cluster entropy
and the outcomes are discussed for arbitrary pairs of power-laws probability
distribution functions of continuous random variables.
