A number of mechanisms have been proposed to explain the
maximum power principle.
I think the most important is the one originally articulated
by Lotka in 1922. Most of the rest of this page is devoted to
Lotka's idea - if you want to look at alternative theories,
scroll right to the bottom.
Lotka noted the importance of energetic resources to
survival - and noted:
[...] in the struggle for existence, the advantage must go to
those whose energy capturing devices are the most efficient
in directing available energy into channels favourable to
the preservation of the species.
- Contribution to the energetics of evolution - Lotka, A. J., 1922
Lotka invoked natural selection - and claimed it would
favour those who got to energy sources fastest and used
them most "efficiently".
Something like this might explain the reason a maximum power
principle applies in biology - but it is not obvious how it
might apply to drainage patterns, turbulent fluid flow, and
to other self-organising systems.
However, I think something very similar does apply to
other self-organising systems.
Many self-organising systems exhibit a crude analog of
the evolutionary process.
In particular the exhibit structures which
exhibit varying degrees of permanence.
Some of these structures are better able to persist
than other ones. Those structures most able to persist
do so, while other structures with less staying power
tend to vanish.
The result is that at any time when you observe the
system there's a tendencey to observe the more stable,
long lived objects, those that are good at persisting.
As you can see, there's an analogy with natural selection
here - everything above also applies to biological systems.
As in the case of biology, the stable structures in self-
organising systems need a flow of energy in order to
maintain their structural integrity, and - since resources
are limited, they tend to compete with one another for
I will next give some examples of non-living systems that
nontheless exhibit this sort of selective process.
In the case of crystal growth, the objects that are good at
persistence tend to be larger crystals. Small crystals
often tend not to last for so long - because they are more
likely to dissolve completely when the level of saturation
in the liquid fluctuates. There are circumstances under
which large crystals can be selectively favoured - while the
smaller crystals tend to have the atoms sucked out of
Turbulent fluid flow shows a similar phenomenon - again with
large vortexes tending to be favoured. If two vortices form
in the same region, the result tends to be unstable - of of
the vortices is inevitably weaker than the other one, and
the stronger vortex sucks resources out of the weaker one
until it collapses. Large vortices can only coexist if they
are far enough apart from each other to not compete with one
another for resources.
Drainage patterns exhibit a similar effect. Rivers remember
where in the landscape they are flowing. Streams compete
with one another for resources. Successful streams become
rivers, and gain more tributaries, a very simple sort of
I think the similarities between these abiotic systems and
the evolutionary process in biology are the main reason why
the maximum power principle appears to apply to both sorts
In both cases structures with varying degrees of persistence
form; these are then subjected to selection - and whether
the structures can maintain their integrty by making rapid
use of environmental resources is an important factor in
which ones survive.
Roderick Dewar has provided an explanation for why dynamical systems
far from equilibrium tend to maximise their rate of entropy gain.
Dewar approaches the subject from the perspective of physics -
and attempts to derive a maximum entropy production principle
from information theory.
His work suggests that rates of high entropy dissipation can
be expected in far-from-equilibrium systems - since an
overwhelmingly large number of possible microstates in the
system are in the process of dissipating entropy rapidly.
Dewar's work is interesting - but his papers are challenging to
understand and interpret.
Tim Tyler |