Rigorous results in non-extensive thermodynamics

Details Rigorous results in non-extensive thermodynamics Rigorous results in non-extensive thermodynamics

1999-08-25

arxiv.org/abs/math-ph/9908025v1

Rev.Math.Phys. 12 (2000) 1305-1324

Physics

Mathematical Physics

21 pages

Scientific paper

10.1142/S0129055X00000526

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

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