order

The asymmetry of local-order and local-disorder

[A holarchical/heirarchical perspective]

Local-order vs. local-disorder

When the spatial, temporal and organisational complexities of systems are explicitly addressed in a hierarchical network thermodynamic context, the action of two principles can be delineated that are both derived from the very same Second Law of Thermodynamics:  "local-order" and "local-disorder" (Choi and Patten 2001). When "local-disorder" dominates, such a system is said to be a perturbed system. When "local-order" dominates, such a system is said to be a less perturbed system. (See definitions below).

This generalisation is important because the relative balance of these two principles applies to any system, regardless of its spatial, temporal and organisational scale or composition. The R/B index has been argued and shown to be a readily measured index of this balance between the two order principles (Choi and Patten 2001).

Some definitions: 

Second Law of Thermodynamics -- Many descriptions exist (e.g. see the Wikipedia description). Ultimately, it is an axiom of the most general kind, that any transformation of matter-energy involves some form of loss. This inefficiency of matter-energy transformation provides the symmetry breaking directionality to time itself.

R/B ratio -- the respiration to biomass ratio, representing a simply measured or estimated index of storage-specific dissipation.

Local-disorder -- the direct action of the Second Law upon all systems ... every energy transformation will result in some (entropic) loss .

Local-order -- the indirect action of the Second Law upon a focal system x{i=0} embedded in an hierarchically structured system spanning from subsystems x{i<0} and supersystems x{i>0}. This is derived from the same law as that of "local-disorder", however it stems from the asymmetrical, fractal-like operation of the second law that cascades through a system that is hierarchically structured (Figure: Second law asymetry;  Choi and Patten 2001). This principle has also been previously identified under non-heirarchical contexts as: "negentropy" (Schrödinger 1945), Least Specific Dissipation principle (Prigogine 1947).

Figure: Second law asymmetry.

Hierarchy -- pertaining to levels of organization, usually defined as an epistemic property to simplify complexity. The question of whether hierarchies are "real" or only mental constructs is  unresolved. Hierarchical concepts are known in the ecological literature (e.g., Allen and Starr 1982; O'Neill et al. 1986) and are the basis for such concepts as "scale" and "grain", expressed in terms of both space and time. Hierarchies of "scale" are nested (supersets, sets, subsets, ... etc.), whereas hierarchies of "control" (e.g., as in the military) are not.

Thermodynamic balance in an hierarchy

The balance between these two antagonistic principles (both derived from the asymmetrical application of the very same law!), where the processes internal to a system (growth and development) are in some quasi-steady state with the processes external to it (exploitative or perturbing influences) is indexed by the R/B ratio (or any other estimate of specific dissipation; Choi and Patten 2001). Any general system can be characterised by a mean and variance of the R/B ratio (e.g., a lake measured repeatedly over time). When local-disorder (perturbing, external influences) dominates, the R/B ratio is elevated and so may be said to be in a state of greater "uncertainty". When local-order dominates (internal processes), the R/B ratio is reduced; such a system may be said to be in a state of lesser "uncertainty". When the magnitude of the R/B (the intensity of energy dissipation) is large, the assumed linear relationship between the gradients and the flows becomes less reliable. This means that the intrinsic pseudo-nonlinearities and nonlinearities of system dynamics may be expected to become more dominant and that a classic bifurcation sequence of the attractive states of (U) may be expected as the R/B ratio increases (Figure: Bifurcation sequence) -- i.e., greater uncertainty.

Figure: Bifurcation sequence 

The immediate consequence of any alterations/manipulations (e.g., nutrient enrichment) to a system is to disturb the balance between local-order and local-disorder, which has the effect of increasing the uncertainty of the relations between all systems (across all hierarchical levels). Thus, the paradox of enrichment (sensu Rosensweig 1971: that enrichment increases dynamical uncertainty) may be expected, in the short term (ecological scales). However, in the long term (evolutionary scales), it was also shown how such manipulations that increase the relative storage (biomass) of a given system could represent a stabilising influence for that system, in that the buffering capacity of the system also increases (see below).

These results are directly applicable to our current struggle to search for a functional example of sustainable exploitation/growth, the current incarnation of the concept of maximum sustainable yield. Maximum sustainable exploitation/growth represents our desire to exploit natural resources as much as possible while simultaneously maintaining these resources for future exploitation (and the currently dominant socio-economic system). As such, it represents an extension of the paradox of enrichment, but to more realistic (complex) situations where many interacting factors are at play (Choi and Patten 2001).

In such a context, the search for "sustainable exploitation/growth" represents a search for the removal of any future uncertainties in the availability of resources -- a search destined to have the same result as the search for a perpetual motion machine. This is because the very act of exploitation is a destabilising influence that increases the uncertainty of the whole dynamical system. Thus, the term "sustainable exploitation" is very much an oxymoron.

However, sustainable exploitation as a guiding principle for orienting and structuring human interactions with its environment represents a more pragmatic stance -- much as the search for a perpetual motion machine has helped develop more efficient engines, so too might the search for sustainable exploitation also help develop more efficient human exploitation of our environment, such that some of the uncertainty associated with our exploitative practises may be reduced. This of course is possible only when all interacting systems become adapted to such relationships. Adaptive responses being on the scale of evolutionary (conservative estimate) to ecological time (optimistic estimate), the rate and extent of human/economic exploitation must be reduced to explicitly account for these much slower processes.

References 

Allen, T.F.H. and T.B. Starr. 1982. Hierarchy: Perspectives for ecological complexity. University of Chicago Press, Chicago.

Choi, J.S. and Patten, B.C. 2001. Sustainable development: lessons from the Paradox of Enrichment. Ecosystem Health 7:163-177.

O'Neill, R.V., DeAngelis, D.L., Waide, J.B. and T.F.H. Allen. 1986. A Hierarchical Concept of Ecosystems. Princeton University Press, Princeton, New Jersey. 253 pp. 

Rosenzweig, M.L. 1971. Paradox of enrichment: destabilization of exploitation ecosystem in ecological time. Science 171:385-387.

Schrödinger, E. 1945. What is life? Cambridge University Press, England. 178 pages.

Prigogine, I. 1947. Etude thermodynamique des phénomènes irréversibles. Desoer, Liège. 143 pages.