Nonextensive Quantum H-Theorem

Abstract

A proof of the quantum $H$-theorem taking into account nonextensive effects on the quantum entropy $S_q^Q$ is shown. The positiveness of the time variation of $S_q^Q$ combined with a duality transformation implies that the nonextensive parameter $q$ lies in the interval [0,2]. It is also shown that the equilibrium states are described by quantum $q$-power law extensions of the Fermi-Dirac and Bose-Einstein distributions. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the quantum distributions contained in the quantum statistics theory.

5 pages, LaTeX

References in corpus (8)

• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Numerical indications of a q-generalised central limit theorem
• Constraining nonextensive statistics with plasma oscillation data
• Nonextensive effects on the relativistic nuclear equation of state
• Power-law statistics and stellar rotational velocities in the Pleiades
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Cited by in corpus (12)

• Thermodynamic Consistency of the $q$-Deformed Fermi-Dirac Distribution in Nonextensive Thermostatics
• Nonextensive statistical effects in the hadron to quark-gluon phase transition
• A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation
• New features of quantum discord uncovered by q-entropies
• Consistent nonadditive approach and nuclear equation of state
• Non-Extensive Quantum Statistics with Particle - Hole Symmetry
• From the hypergeometric differential equation to a non linear Schrödinger one
• Nonextensive Nuclear Liquid-Gas Phase Transition
• Generalized Ensemble Theory with Non-extensive Statistics
• Solutions for a q-generalized Schrödinger equation of entangled interacting particles
• Nonextensive Kinetic Theory and H-Theorem in General Relativity
• Non-Extensive Behaviour of the QCD Strong Coupling Constant