Extended Prigozhin theorem: method for universal characterization of complex system evolution

TL;DR

This paper extends the Prigozhin theorem to provide a universal framework for characterizing the evolution of complex stochastic systems, distinguishing between accelerator and decelerator types through energy-based phase parameters.

Contribution

The paper introduces an extended Prigozhin theorem applicable to arbitrary nonlinear systems, incorporating energy-based phase parameters and differentiating system types for universal disorder characterization.

Findings

Derived relations for entropy production near stationary states.

Extended theorem applies to both accelerator and decelerator systems.

Classical theorem limited to linear decelerator description.

Abstract

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigozhin theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigozhin theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigozhin theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.