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A multi-parametric version of the nonadditive entropy $S_{q}$ is introduced.This new entropic form, denoted by $S_{a,b,r}$, possesses many interestingstatistical properties, and it reduces to the entropy $S_q$ for $b=0$,$a=r:=1-q$ (hence Boltzmann-Gibbs entropy $S_{BG}$ for $b=0$, $a=r \to 0$). Theconstruction of the entropy $S_{a,b,r}$ is based on a general group-theoreticalapproach recently proposed by one of us \cite{Tempesta2}. Indeed, essentiallyall the properties of this new entropy are obtained as a consequence of theexistence of a rational group law, which expresses the structure of $S_{a,b,r}$with respect to the composition of statistically independent subsystems.Depending on the choice of the parameters, the entropy $S_{a,b,r}$ can be usedto cover a wide range of physical situations, in which the measure of theaccessible phase space increases say exponentially with the number of particles$N$ of the system, or even stabilizes, by increasing $N$, to a limiting value.This paves the way to the use of this entropy in contexts where a system"freezes" some or many of its degrees of freedom by increasing the number ofits constituting particles or subsystems.

A new entropy based on a group-theoretical structure