The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn \cite{tawn}, Joe and Hu \cite{joe+hu} and Fougères et al. \cite{fougeres+nolan+rootzen}. The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li \cite{li}.
There exist different formulations of the irreversible thermodynamics. Depending on the distance from the equilibrium state and on the characteristic time the main theories are the classical theory (CIT), the thermodynamics with internal variables (IVT) and the extended theory (EIT). Sometimes it is not easy to choose the proper theory and to use it efficiently with respect to applied problems considering different fields of interest. Especially EIT is explained mainly for very special choice of the dissipative fluxes under specific presumptions. The paper tries to formulate EIT and IVT in a simple, unified but general enough form. The basic presumptions for EIT are shown and discussed, further a possible generalization is proposed. The formulation allows the integration of iVT and EIT even for the mixture of chemically interacting components and diffusion. The application of the formulation is demonstrated on an example. and Obsahuje seznam literatury