Tatsuaki Wada

Information geometry of q-Gaussian densities and behaviors of solutions to related diffusion equations*

This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss thermostatistical structure with information geometry on a manifold of generalized exponential densities. A dualistic relation between the two existing formalisms is elucidated. Next by equipping the manifold of q-Gaussian densities with such a structure, we derive several physically and geometrically interesting properties of the solutions. The manifold is proved invariant and attracting for the evolving solutions, which play crucial roles in our analysis. We demonstrate that the moment-conserving projection of a solution coincides with a geodesic curve on the manifold. Further, the evolutional velocities of the second moments and the convergence rate to the manifold are evaluated in terms of the Bregman divergence. Finally we show that the self-similar solution is geometrically special in the sense that it is simultaneously geodesic with respect to the mutually dual two affine connections.

Influence of Exposure to CO, CO2 and H2O on the Stability of GaAs Photocathodes

The influence of CO, CO2 and H2O gases on the stability of negative-electron-affinity (NEA) GaAs photocathodes during operation is investigated in the present work. We have found that exposure both to H2O and CO2 decreases the photocurrent of the photocathode. However, exposure to CO, which is known as a harmful gas to various photocathodes, has little effect on the photocathode stability. Furthermore, the effects of these gases on the restoration of the photocurrent by additional cesium deposition are investigated. These results are discussed with regard to the Cs/O activation layer which plays an important role in NEA GaAs photocathodes.

A two-parameter generalization of Shannon–Khinchin axioms and the uniqueness theorem

Abstract Based on the one-parameter generalization of Shannon–Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti–Jagannathan difference operator.

Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics

AbstractThe asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the κ-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the κ-Gaussian function is not a scale invariant solution of the generalized diffusive equation. Notwithstanding, several numerical simulations, with different initial conditions, show that the solutions asymptotically approach to the κ-Gaussian function. Simple argument based on a time-dependent transformation performed on the related κ-generalized Fokker-Planck equation, supports this conclusion.

Canonical Partition Function for Anomalous Systems Described by the κ-Entropy

Starting from the

Gas sensitive properties of copperphthalocyanine thin films

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Discrete-time quantum walk with feed-forward quantum coin

-distribution function, obtained by applying the maximal entropy principle to the

A non self-referential expression of Tsallis' probability distribution function

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Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq

-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical

Thermodynamic stability conditions for nonadditive composable entropies

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