In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are found in the context of this approach. Solutions of the sets of linear equations with respect to fluxes and their higher-order time derivatives allow the coefficients of diffusion and reaction rate constants to be established as functions of size of the nanosystems in which these reactions occur. The Maxwell-Cattaneo and Jeffreys constitutive equations, as well as the higher-order constitutive equations, which describe the processes in reaction-diffusion systems, are obtained.

Generalization of the variational formulation of the Onsager–Machlup thermodynamic theory of fluctuation is considered. Within the framework of variational theory, we introduce the time-dependent generalized normal distribution and Hamilton–Jacobi equation. The family of higher-order partial differential equations, which generalize classical Fokker–Planck equation, is considered. It is shown that proposed theory can be used for describing anomalous diffusion.

The effect of precursor on the properties of nanosized sulfide catalysts prepared by the in situ decomposition of nickel–tungsten compounds is studied. Precursors are nickel-thiotungsten...