About a nonadditivity of energy and entropy

The mathematical expression of nonadditivity X(1 ?? 2) = X(1) + X(2) + ??X(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and ?? is hoped to be a parameter characterising the nonadditive property of the composite system (1 ?? 2). Here we show that this relationship cannot hold exactly. In general, ?? in this expression inevitably depends on how a given system with constant X(1 ?? 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.