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When is a quantity additive, and when is it extensive?

Touchette, Hugo - In: Physica A: Statistical Mechanics and its Applications 305 (2002) 1, pp. 84-88

The difference between the terms additivity and extensivity, as well as their respective negations, is critically … analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are also …

Persistent link: https://www.econbiz.de/10010871587

Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond

Ván, P. - In: Physica A: Statistical Mechanics and its Applications 365 (2006) 1, pp. 28-33

It is proved that the only additive and isotropic information measure that can depend on the probability distribution and also on its first derivative is a linear combination of the Boltzmann–Gibbs–Shannon and Fisher information measures. Power-law equilibrium distributions are found as a...

Persistent link: https://www.econbiz.de/10011057662

On generalized entropy measures and pathways

Mathai, A.M.; Haubold, H.J. - In: Physica A: Statistical Mechanics and its Applications 385 (2007) 2, pp. 493-500

entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that … the natural process is non-additivity, important, for example, in statistical mechanics [C. Tsallis, Possible … dynamics—an unsolved problem, Pramana 64 (2005) 635–643.], even in product probability property situations and additivity can …

Persistent link: https://www.econbiz.de/10011060411

Monotonically equivalent entropies and solution of additivity equation

Gorban, Pavel - In: Physica A: Statistical Mechanics and its Applications 328 (2003) 3, pp. 380-390

-form (the form of sum over the states), and additivity (for composition of independent subsystems). All the entropies, which …

Persistent link: https://www.econbiz.de/10010589341

Thermodynamical entropy (and its additivity) within generalized thermodynamics

Almeida, M.P. - In: Physica A: Statistical Mechanics and its Applications 325 (2003) 3, pp. 426-438

This is an analysis of the thermodynamical entropy of systems with finite heat baths and of its additivity. It is …

Persistent link: https://www.econbiz.de/10010591829

Twist of fractional oscillations

Stanislavsky, Aleksander A. - In: Physica A: Statistical Mechanics and its Applications 354 (2005) C, pp. 101-110

Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations...

Persistent link: https://www.econbiz.de/10010871613

The relationship between the fractional integral and the fractal structure of a memory set

Ren, Fu-Yao; Yu, Zu-Guo; Zhou, Ji; Mehaute, Alain Le; … - In: Physica A: Statistical Mechanics and its Applications 246 (1997) 3, pp. 419-429

It is shown that there is no direct relation between the fractional exponent v of the fractional integral and the fractal structure of the memory set considered, v depends only the first contraction coefficient χ1 and the first weight P1 of the self-similar measure (or infinite self-similar...

Persistent link: https://www.econbiz.de/10011058219

Laplace transform analysis of a multiplicative asset transfer model

Sokolov, Andrey; Melatos, Andrew; Kieu, Tien - In: Physica A: Statistical Mechanics and its Applications 389 (2010) 14, pp. 2782-2792

in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic …

Persistent link: https://www.econbiz.de/10011060852

Radial anomalous diffusion in an annulus

Wang, Shaowei; Zhao, Moli; Li, Xicheng - In: Physica A: Statistical Mechanics and its Applications 390 (2011) 20, pp. 3397-3403

In this study, time fractional radial diffusion has been modeled in cylindrical coordinates in order to analyze the anomalous diffusion in an annulus. By using an integral transform technique, the analytical solution of the concentration distribution formula is obtained. The establishing of the...

Persistent link: https://www.econbiz.de/10011062156

The non-integer operation associated to random variation sets of the self-similar set

Ren, Fu-Yao; Liang, Jin-Rong - In: Physica A: Statistical Mechanics and its Applications 286 (2000) 1, pp. 45-55

When memory sets are random variation sets of the self-similar set and the total number of remaining states in each stage of the division of this set is normalized to unity, the corresponding flux and fractional integral are “robust” and stable under some conditions. This answers an open...

Persistent link: https://www.econbiz.de/10011064440