Related papers: A new one parameter deformation of the exponential…

In the present effort we show that $S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)$ is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy $S_0=-k_B \int d^3p n \ln n$ and…

We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa}:z\mapsto \exp(z)+\kappa$ escapes to infinity under iteration. In particular, we show that every path-connected component of this…

In this paper, we show that the causally connected $4$-dimensional line element of the $\kappa$-deformed Minkowski space-time induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order…

We have investigated the proof of the $H$ theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 72}, 036108,…

Gallager and Van Voorhis have found optimal prefix-free codes $\kappa(K)$ for a random variable $K$ that is geometrically distributed: $\Pr[K=k] = p(1-p)^k$ for $k\ge 0$. We determine the asymptotic behavior of the expected length ${\rm…

The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa}(f)=\frac{1}{2\kappa}\sum_i (f_i^{1-\kappa}-f_i^{1+\kappa})$ with $0<\kappa<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is…

This paper shows that the recently proposed $\kappa$-$\mu$ shadowed fading model includes, besides the $\kappa$-$\mu$ model, the $\eta$-$\mu$ fading model as a particular case. This has important relevance in practice, as it allows for the…

We study numerically the thermal conductivity coefficient $\kappa$ as a function of system length $L$ for several different quasi one dimensional models: classical gases of hard spheres with both longitudinal and transverse degrees of…

This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that the polytropic…

In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we…

Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized…

We present the alternative derivation of the excluded volume equation. The resulting equation is mathematically identical to the one proposed in the preceding paper. As a result, the theory reproduces well the observed points by SANS (small…

In this paper we show that the Cutkosky cutting rules are still valid term by term in the expansion in powers of $\kappa$ of the $\kappa$-deformed 1-loop correction to the propagator. We first present a general argument which relates each…

This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion of non-local operators that give power law damping as…

We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…

We study the distribution of the eigenvalue condition numbers $\kappa_i=\sqrt{ (\mathbf{l}_i^* \mathbf{l}_i)(\mathbf{r}_i^* \mathbf{r}_i)}$ associated with real eigenvalues $\lambda_i$ of partially asymmetric $N\times N$ random matrices…

In the following work we will introduce and discuss in detail a particular model of complex $\kappa$-deformed scalar field, whose behaviour under C, P , T transformation is particularly transparent from both a formal and phenomenological…

Kaniadakis deformed \kappa-mathematics is an area of mathematics that has found relevance in the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay \kappa-differential equation is…

We rediscuss recent derivations of kinetic equations based on the Kaniadakis' entropy concept. Our primary objective here is to derive a kinetical version of the second law of thermodynamycs in such a $\kappa$-framework. To this end, we…

In this work we propose a robust methodology to mitigate the undesirable effects caused by outliers to generate reliable physical models. In this way, we formulate the inverse problems theory in the context of Kaniadakis statistical…