On concave entropies of discrete systems

A new class of entropy functions of discrete systems, the class of concave entropies, is introduced. Each concave entropy function satisfies the fundamental axioms of general entropies. The Shannon and trigonometric entropies belong to the class of concave entropies. Each of the classes of Renyi and polynomial entropies contains a subclass of concave entropies. A sufficient condition is given, under which the total entropy tends to ∞, when the number N of probability components approaches ∞.