The maximum entropy production principle in the evolution of the macrosystems: some new results
DOI:
https://doi.org/10.15587/1729-4061.2014.31345Keywords:
maximum entropy production principle, Ziegler's principle, evolution of complex systems, macrosystemsAbstract
Closed non-equilibrium macrosystems, which are in the process of evolution to the equilibrium state, subject to the maximum entropy production principle are considered in the paper.
A procedure for direct calculation of entropy production in an arbitrary step of evolution is developed. In accordance with the maximum entropy production principle, the nonlinear equations of the distribution dynamics in the non-equilibrium closed system are obtained. It is shown that the development trajectory of such system is entirely determined by the nature of the initial distribution and distribution in the equilibrium state. Far from the equilibrium state, a decisive role in the evolution equation is played not by the difference between these values, but the difference of their logarithms.
The definition of "internal" system time is given.
A theorem, which states that distribution of elements by the phase space cells, which keeps a sum of the logarithms of their number constant is implemented at each time point for the closed non-equilibrium system, developed in accordance with the maximum entropy production principle is proved. Its formulation for the case of continuous distributions is given. The connection with the Liouville's theorem is shown.
Dynamic invariant of the evolution of closed systems, evolving in accordance with the maximum entropy production principle is defined.
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