Dual description of nonextensive ensembles
Jan Naudts
Abstract
In the case of a system with an unbounded hamiltonian the entropic index q of non-extensive thermodynamics has an upperbound qc>1 beyond which the formalism becomes meaningless. The expression 1/(qc-1) is the dimension of the state space (i.e. the manifold of density matrices) in the context of non-commutative geometry. For q=qc an ultraviolet cutoff E< Eub is needed to guarantee the existence of the equilibrium density matrix. Duality between q>1 and q<1-statistics via a q --> 1/q transformation is established. It leads to an overall picture in which the meaning of both q>1-statistics and q<1-statistics is clarified.
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