 99307 Jan Naudts
 Rigorous results in nonextensive thermodynamics
(52K, latex)
Aug 23, 99

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Abstract. This paper studies quantum systems with a finite number of degrees of
freedom in the context of nonextensive thermodynamics. A trial density
matrix, obtained by heuristic methods, is proved to be the equilibrium
density matrix. If the entropic parameter q is larger than 1 then
existence of the trial equilibrium density matrix requires that q is
less than some critical value q_c which depends on the rate by which
the eigenvalues of the hamiltonian diverge. Existence of a unique
equilibrium density matrix is proved if in addition q<2 holds. For q
between 0 and 1, such that 2<q+q_c, the free energy has at least one
minimum in the set of trial density matrices. If a unique equilibrium
density matrix exists then it is necessarily one of the trial density
matrices. Note that this is a finite rank operator, which means that in
equilibrium high energy levels have zero probability of occupancy.
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