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: