1. introduction
Physics offers a robust perspective on the role of subsystem-correlations in free-energy driven emergence of both analog and digital complexity. For instance, the biological literature has spent much time thinking about evolutionary selection operating on post-pair collections of organisms like families, interaction-groups, and species\cite{Okasha2008} even though practical quantitative work cuts through the ``Ptolemaic epicycles" of organism-centricity by focusing directly on the dynamics of code-pools\cite{Nowak2010} instead.
Our evolving view of states for condensed matter\cite{Sethna2006} serves as entry-point for a complementary physical approach. From the perspective of subsystem B, one might describe complete ignorance of an evolving subsytem A as perfectly symmetric since it attributes to A no special locations, directions, or excitations. Interactions that correlate subsystem B with an evolving subsystem A might provide information to B about specific locations, directions, and excitations in subsystem A, thereby breaking that perfect symmetry.
Gibb's dimensionless thermodynamic-availability\cite{Gibbs1873}, in modern terms known as Kullback-Leibler divergence i.e. mutual-information with respect to an arbitrary prior, is a measure of the correlation-information between subsystems A and B. The 2nd Law requires that our correlations with a subsystem A from which we are isolated can only decrease over time\cite{Lloyd89b}, but even then the time evolution of A's thermodynamic availability can give rise to the emergence in A of new symmetry breaks, or even a hierarchy of such breaks.
On the molecular level\cite{Ziman1979}, for instance, the relatively-featureless isotropic-symmetry of liquid water may on cooling first be broken by local translational pair-correlations (resulting in spherical reciprocal-lattice shells) as the liquid turns to polycrystal ice, and eventually by global translational and rotational ordering (resulting in reciprocal-lattice spots) as the ice becomes a single crystal. Partly along the way to single-crystal form a quasicrystal phase might have rotational without translational ordering, while a random-layer lattice might have rotational and translational ordering in one ``layering" direction only. Thus even within a single layer of organization, broken symmetries (often associated with a spatial gradient and/or boundary) play a role in the local development of order.
Complex systems often boast a hierarchical set of broken symmetries with associated gradients and/or boundaries. For instance a temperature-gradient marks the ``level-1" symmetry break that defines the center of a collapsing star system, within which local gravitational wells and condensed-matter surfaces associated with orbiting bodies (including planets) define ``level-2" symmetry-breaks.
In these gradients of our own planet a small number of (plausibly only six) additional broken-symmetries\cite{Anderson72}, again marked by the edges of a hierarchical series of physical subsystem-types, underlie the delicate correlation-based complexity of that interface-phenomenon that we call life. In this paper we explore how, by considering more than one level at a time, order-parameters\cite{Sethna2006} associated with these broken symmetries (which like standing-biomass and body-count are already quite useful) might help us broaden our definitions of community health\cite{pf.simplex}.
Related references:
Samir Okasha (2008) Evolution and the levels of selection (Oxford University Press, UK).
Martin A. Nowak, Corina E. Tarnita & Edward O. Wilson (2010) Nature 466, 1057-1062 abstract supplement.
James P. Sethna (2006) Entropy, order parameters and complexity (Oxford U. Press, Oxford UK) (e-book pdf).
J.W. Gibbs (1873) "A method of geometrical representation of thermodynamic properties of substances by means of surfaces", reprinted in The Collected Works of J. W. Gibbs, Volume I Thermodynamics, ed. W. R. Longley and R. G. Van Name (New York: Longmans, Green, 1931) footnote page 52.
Seth Lloyd (1989) "Use of mutual information to decrease entropy: Implications for the second law of thermodynamics", Physical Review A 39, 5378-5386 (link).
J. M. Ziman (1979) Models of disorder: The theoretical physics of homgeneously disordered systems (Cambridge U. Press, Cambridge UK).
P. W. Anderson (1972) "More is different", Science 177:4047, 393-396 pdf.
P. Fraundorf (2008) "A simplex model for layered niche-networks", Complexity 13:6, 29-39 abstract e-print.