Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be formulated in terms of kappa-deformed exponential functions together with the associated deduced logarithmic functions.Comment: Latex, 12 page

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A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of Cram´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities

Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.

The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche's stability condition. The entropies of Tsallis' nonextensive thermostatistics are taken as examples.