Sunday, November 4, 2012

Finding similar ideas in other fields - ecology and thermodynamics of complex systems

I very much like to find connections between ideas in different fields. The Wikipedia page on Ecology contains the following quote:
System behaviors must first be arrayed into levels of organization. Behaviors corresponding to higher levels occur at slow rates. Conversely, lower organizational levels exhibit rapid rates. For example, individual tree leaves respond rapidly to momentary changes in light intensity, CO2 concentration, and the like. The growth of the tree responds more slowly and integrates these short-term changes.
O'Neill, et al., A Hierarchical Concept of Ecosystems, Princeton University Press, p. 253 (1986).
This is not much unlike the microscopic and macroscopic descriptions of a material system. Small-scale fluctuations in the microscopic arrangement of a material often don't significantly impact the macroscopic qualities of this system [1]. Rather, many small-scale changes must occur in concert to cause a large-scale change. For example, the momenta and positions of various gas molecules in a container at equilibrium with its surroundings may change about some average, but the pressure of the gas on the container's walls will not. If the average molecular speed changes, though, pressure will likely change as well.

In addition, if the interaction between the microscopic constituents is nonlinear, it becomes much more likely that small changes in the microscopic description will result in macroscopic changes as well.

[1] In fact, most fluctuations are dissipated by the system. If the system is in equilibrium with its environment, then energy conservation, among other things, implies that a fluctuation away from equilibrium of a local volume inside a system will eventually be "smoothed out" by the system. This is an important property of complex systems known as the fluctuation-dissipation theorem.