Generalized Entropies Obtained from Extensivity Principle

We present a derivation of generalized entropy measures based on the thermodynamic principle of extensivity, independent of heuristic or purely phenomenological arguments. Starting from the scaling behaviour of entropy with particle number in the thermodynamic limit, we derive known entropy forms including the Boltzmann–Gibbs and Tsallis entropies, as well as the entropy classes characterized by the Hanel–Thurner scaling exponents ccc and ddd. A novel two-parameter entropy is introduced, which captures systems exhibiting both finite-size effects and constrained phase space dynamics. This entropy reduces to known forms in limiting cases and provides a potential framework for describing complex systems with strong correlations, such as biological networks or constrained quantum systems. Our approach emphasizes the role of relative fluctuations and asymptotic scaling in determining the functional form of entropy, suggesting a unified thermodynamic origin for a spectrum of generalized entropies. Possible applications and implications for statistical physics and information theory are discussed.