Jan Naudts
Rigorous results in non-extensive thermodynamics
(52K, latex)

ABSTRACT.  This paper studies quantum systems with a finite number of degrees of 
freedom in the context of non-extensive 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.