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the founder of the nonequilibrium thermodynamics, Prigogine, examined in detail
the formation of ordered structures in the Belousov-Zhabotinsky media. Because
these processes require energy inflow or outflow of entropy (its dissipation),
Prigogine called such systems and the structures emerging in them dissipative.
These processes are also called nonequilibrium phase transitions.
Certain conditions need to be satisfied for the occurrence of nonequilibrium
phase transitions that are manifested by the formation of new dissipative structures:
(A) Dissipative structures can be formed only in open systems because only in such
systems energy inflow is possible compensating for losses due to dissipation
and ensuring the existence of more ordered states.
(B) Dissipative structures arise in macroscopic systems, i.e., systems consisting of
a large number of elements (atoms, molecules, macromolecules, cells, etc.).
This makes collective interactions possible.
(C) Dissipative structures arise only in systems described by nonlinear equations
for macroscopic functions. Examples are kinetic equations, such as the
Boltzmann equation, and equations of gas dynamics and hydrodynamics.
(D) For the occurrence of dissipative structures, nonlinear equations must allow for
change of symmetry of the solution under certain values of control parameters.
This change is manifested, for example, in the transition from the molecular to
the convective heat transfer in Benard cells.
3. The system should show both positive and negative feedback. Processes in a
dynamic system tend to change the basic relations between the components of the
system involved in these processes. Such changes can be called changes at the
output of the system. At the same time, these components are required for starting
up the processes taking place in the system; they are thus the parameters at the
system's input. If changes at the output of the system affect the input parameters
such that changes at the output are amplified, we are dealing with positive feedback
or autocatalytic growth. Negative feedback is a situation where the dynamic
processes in the system maintain a constant state at the output. In a general case
dynamic systems with positive and negative feedback are modeled by nonlinear
differential equations. This reflects the nonlinear nature of systems capable of self-
organization—apparently the fundamental property of the system, which deter-
mines its ability to self-organize.
6.3.1 Some Details: The Nonlinearity of the Surrounding
World
The world around us is complex. This complexity is manifested in scientific
research, technology, and everyday life. At the same time, human consciousness
has always been characterized by the desire to identify in this complex world a
simple component reflecting its essential nature.
