Two forms of self-similarity as a fundamental feature of the power-law dielectric response

A mechanism to derive multi-power law functions: An application in the econophysics framework

“…Thus, the deformed exponential exp {κ, r} (x) interpolates with continuity between the standard exponential exp(x) ≃ 1 + x, for x → 0, and the power law |x| −s with slope s = −1/(r ± |κ|), for x → ±∞. Finally, accounting for the solution (2.5), the entropy (2.1) assumes the form 6) which recovers, in the limit (κ, r) → (0, 0), the Shannon-Boltzmann-Gibbs entropy S = − p(x) ln p(x) dx. This entropic form, introduced previously in literature in [13,14,15], is known as the Sharma-Taneja-Mittal information measure and has been applied recently in the formulation of a possible thermostatistics theory [16,17].…”

Relaxation dynamics of the fastest channel in multichannel parallel relaxation mechanism

“…It has been shown [25] that in case of deterministic number m x x the only possible probability distributions pbà for the eective relaxation rateb à b are completely asymmetric L evy-stable laws a with the parameter 0`a`1 together with degenerate caseb const obtained when a 3 1. These distributions are easily de®ned by their Laplace transforms:…”

Superdomain dynamics in ferroelectric-ferroelastic films: Switching, jamming, and relaxation

“…However, Weron shows that the stretched exponential is merely a special limiting approximation to a more general power law. [60][61][62] She points out that the exponential arises when one neglects the distribution of waiting times for the relaxing dipoles and when one treats each relaxing dipole as independent, as contrasted with cluster behavior. The problem with many switching models (e.g., Avrami and nucleationfrustrated) is that they assume all relaxation starts at the same time t=0; that is, there is no "waiting time."…”