Chapter 15
Ordering Theory
We have seen that the formation and maintenance of
self-organizing systems are compatible with the laws of physical
chemistry.
—Ilya Prigogine
Summary Order can be measured in a system, whether it be the order on your desk
or the order within your body. For open systems with activity, ordering is a natural
process, such as the simple crystallization of a salt initially dissolved in water, or
as the convoluted evolution of life systems. In general, the necessary elements for
ordering can be spelled out, and examples given, including DNA replication, protein
synthesis, and brain operations. Throughout the Universe’s development, thresholds
for rapid changes in the rates of ordering have occurred. Life formation is one, and
so is the invention of the printing press. For any open subsystem, ordering can lead
to complexity, with new ‘rules’ governing optimized behavior.
15.1 Defining Order
We have already introduced the idea of entropy in a system. The statistical, rather
than the thermodynamic, definition of entropy is better because it is defined even
when thermodynamic quantities are ill-defined. For systems with a fixed total energy
and given microstates, the entropy of that system is proportional to the logarithm
of the number of ways that system might be found by a redistribution of its
fundamental particles within its microstates. A microstate of the system is a possible
quantum state for the system’s particles, but included are only those quantum states
whose occupation can be varied by interactions within the system and with the
particle’s local environment. A fundamental particle of a system is a localizable
entity that has identifiable and unchanging properties, at least over observation
times. By implication, interactions with the particle will provide insufficient energy
to change the internal properties of the particle. Ordering occurs when the entropy
of a system drops.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3_15
595
Ordering Theory
We have seen that the formation and maintenance of
self-organizing systems are compatible with the laws of physical
chemistry.
—Ilya Prigogine
Summary Order can be measured in a system, whether it be the order on your desk
or the order within your body. For open systems with activity, ordering is a natural
process, such as the simple crystallization of a salt initially dissolved in water, or
as the convoluted evolution of life systems. In general, the necessary elements for
ordering can be spelled out, and examples given, including DNA replication, protein
synthesis, and brain operations. Throughout the Universe’s development, thresholds
for rapid changes in the rates of ordering have occurred. Life formation is one, and
so is the invention of the printing press. For any open subsystem, ordering can lead
to complexity, with new ‘rules’ governing optimized behavior.
15.1 Defining Order
We have already introduced the idea of entropy in a system. The statistical, rather
than the thermodynamic, definition of entropy is better because it is defined even
when thermodynamic quantities are ill-defined. For systems with a fixed total energy
and given microstates, the entropy of that system is proportional to the logarithm
of the number of ways that system might be found by a redistribution of its
fundamental particles within its microstates. A microstate of the system is a possible
quantum state for the system’s particles, but included are only those quantum states
whose occupation can be varied by interactions within the system and with the
particle’s local environment. A fundamental particle of a system is a localizable
entity that has identifiable and unchanging properties, at least over observation
times. By implication, interactions with the particle will provide insufficient energy
to change the internal properties of the particle. Ordering occurs when the entropy
of a system drops.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3_15
595