Generalized entropy: Its properties

Attempts to generalize the Boltzmann form of the entropy are reviewed. The recent generalized entropy of Prigogine and coworkers is outlined. Its comparison with the Boltzmann form is discussed and the argument is made that the Boltzmann form cannot be generalized to long-range correlations. Evidence is shown by the moderate density calculation of Allen. The convexity of the generalized entropy is discussed as well as the extension to open systems.