Density matrix for a consistent non-extensive thermodynamics

Abstract

Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the bosonic case the corresponding operators satisfy a deformed bosonic algebra and the hamiltonian involves interacting terms in powers of $a_j^{†}{a}_j$ standard creation and annihilation operators. For the unnormalized density matrix we obtain a nonlinear equation that leads to a two-parameter solution relevant to anomalous diffusion phenomena.

arXiv comment9 pages

References in corpus (12)

• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• The Tsallis Distribution in Proton-Proton Collisions at $\sqrt{s}$ = 0.9 TeV at the LHC
• Entropies based on fractional calculus
• Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
• Generalized thermodynamics of q-deformed bosons and fermions
• Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
• Thermodynamic Consistency of the $q$-Deformed Fermi-Dirac Distribution in Nonextensive Thermostatics
• Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution
• Non extensive thermodynamics and neutron star properties
• Asymptotic solutions of a nonlinear diffusive equation in the framework of $\kappa$-generalized statistical mechanics
• A simple mathematical model for anomalous diffusion via Fisher's information theory
• Scalar curvature of systems with fractal distribution functions