A new entropy based on a group-theoretical structure

A multi-parametric version of the nonadditive entropy S-q is introduced. This new entropic form, denoted by S-a,S-b,S-r, possesses many interesting statistical properties, and it reduces to the entropy Sq for b = 0, a = r := 1 - q (hence Boltzmann-Gibbs entropy S-BG for b = 0, a = r -> 0). The construction of the entropy Sa,b,r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of Sa,b,r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy Sa,b,r can be used to cover a wide range of physical situations, in which the measure of the accessible 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 the size of the phase space does not,increase as fast as the number of its constituting particles (or subsystems) increases.