The problem of calculating thermodynamic potentials in statistical mechanics by using the method of self-similar approximations developed by the authors is considered. An emphasis is made on the search for a regular procedure of defining higher-order terms providing a good accuracy and stability...

The method of self-similar approximation is extended here to the problem of calculating thermodynamic potentials in statistical mechanics. To formulate an optimal scheme of the method, we compare its different variants connected with different definitions of governing functions and damping...

We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes into account (i) the price formation delay between...

A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A chaotic diffusion process intermixes these regions by...

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control...

Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat. It is shown that, despite arbitrary strong interactions...

Stability of thermodynamic states is analysed for the heterophase model with spin reorientations, earlier proposed by the authors. Reorientation points and Curie points are determined and the critical indices are found in these points. The behaviour of the main thermodynamic characteristics is...

The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the probability distribution of patterns. Then the most...