In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and investigate some related properties. Some inequalities involving the generalized are pointed out as well.

We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among partitions characterised by probability distribution functions $P$ and $Q$. The measure is illustrated with clusters generated pairs of fractional Brownian motions Hurst exponents $H_1$ $H_2$ respectively. For subdiffusive, normal superdiffusive sequences, relat...