Stochastic storage models and noise-induced phase transitions

The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes restrictions on the description of the phase transition problem where the system is to overcome some finite potential barrier, or systems with finite size where the fluctuations are comparable with the size of a system. We suggest a complementary stochastic description of physical systems based on the mathematical stochastic storage model with basic notions of random input and output into a system. It reproduces statistical distributions typical for noise-induced phase transitions (e.g. Verhulst model) for the simplest (up to linear) forms of the escape function. We consider a generalization of the stochastic model based on the series development of the kinetic potential. On the contrast to Gaussian processes in which the development in series over a small parameter characterizing the jump value is assumed [Stratonovich R.L., Nonlinear Nonequilibrium Thermodynamics, Springer Series in Synergetics, vol.59, Springer Verlag, 1994], we propose a series expansion directly suitable for storage models and introduce the kinetic potential generalizing them.Comment: 10 pages, 1 figur

Development of the Theory of Capitalist Crises: Political Economy Traditions and Modernity

The article discusses the development history of the theory of economic crises under capitalism conditions. The author believes that economic science is being developed in two directions. The first direction is represented by science schools that deny any objective grounds for crises of overproduction in the market economy and develop new models of crisis-free growth. The opposite direction is supported by science schools acknowledging the existence of objective causes of crises, which is of practical significance for development of effective anti-crisis measures. The study is summarized by the conclusion about actualization of the political economy approach to analysis of the recent global crisis and its consequences. Its implementation anticipates special attention to different versions of overaccumulation of capital which played a key role in the origin of crisis processes in the world economy