Imperial College Complexity & Networks Seminar
Speaker: Dr Rudolf A. Hanels, Section for Science of Complex Systems , Medical University of Vienna
Title: A theory of generalized entropies
Abstract: Generalized entropies have been introduced for describing characteristic non-exponential distribution functions that frequently appear in the context of non-extensive Systems. The controversy over the fundamental necessity of generalized entropies however can be decided in their favor. In contrast to equilibrium theories of systems the theory of generalized entropies has to distinguish carefully between so called “generalized extensive entropies” and the “entropy functionals” appearing in generalized MEPs. These MEPs however can be deduced from traditional maximum configuration arguments as they have been applied since Boltzmann. The key to understanding both notions of generalized entropies, for instance in (not necessarily stationary) systems with infinite memory (memory that starts with initialization of a process) is the way phase-space grows with system size and has little to do with observable distribution functions. In fact examples exist where systems requiring generalized entropies possess Gaussian distribution functions