Composition law of κ\kappa-entropy for statistically independent systems

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 shown that, for a statistical system described by the probability distribution $f=\{ f_{ij}\}$, made up of two statistically independent subsystems, described through the probability distributions $p=\{ p_i\}$ and $q=\{ q_j\}$, respectively, with $f_{ij}=p_iq_j$, the joint entropy $S_{\kappa}(p\,q)$ can be obtained starting from the $S_{\kappa}(p)$ and $S_{\kappa}(q)$ entropies, and additionally from the entropic functionals $S_{\kappa}(p/e_{\kappa})$ and $S_{\kappa}(q/e_{\kappa})$, $e_{\kappa}$ being the $\kappa$-Napier number. The composition law of the $\kappa$-entropy is given in closed form, and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the $\kappa \rightarrow 0$ limit.Comment: 14 page

Thermal diffusivity of amorphous plastic materials

The paper presents thermal diffusivity data on amorphous plastic materials, obtained by means of a method previously developed by the authors. This methods ensures high sensitivity (<1%) and good reproducibility (<3%

Thermal Conductivity of Isotopically Enriched 28Si Revisited

The thermal conductivity of isotopically enriched 28Si (enrichment better than 99.9%) was redetermined independently in three laboratories by high precision experiments on a total of 4 samples of different shape and degree of isotope enrichment in the range from 5 to 300 K with particular emphasis on the range near room temperature. The results obtained in the different laboratories are in good agreement with each other. They indicate that at room temperature the thermal conductivity of isotopically enriched 28Si exceeds the thermal conductivity of Si with a natural, unmodified isotope mixture by 10&#61617;2 %. This finding is in disagreement with an earlier report by Ruf et al. At &#61566;26 K the thermal conductivity of 28Si reaches a maximum. The maximum value depends on sample shape and the degree of isotope enrichment and exceeds the thermal conductivity of natural Si by a factor of &#61566;8 for a 99.982% 28Si enriched sample. The thermal conductivity of Si with natural isotope composition is consistently found to be &#61566;3% lower than the values recommended in the literature