Phase Transitions As A Metaphor for the Genesis of Complexity

phase diagram of water

You might have enjoyed reading the novel Cat's Cradle by Kurt Vonnegut. In this book, an eccentric scientist Felix Hoenikker invents an ultimate weapon of war, a small crystal of a fictitious phase of water called ice-nine that is solid at room temperature and which, if thrown into an ocean, would doom the human race by converting the liquid ocean to solid ice-nine. From what you learn in Physics 363, could such a crystal exist in principle, that could convert a liquid to solid phase?

While thinking about that problem, contemplate the experimentally determined phase diagram of water as shown above and appreciate the many possible phases that exist as temperature and pressure are varied. Note that there is actually an ice-nine, the phase region in the upper left labeled by the Roman numeral IX, but it exists only for pressures much greater than atmospheric pressure and for temperatures less than room temperature. There are 15 known crystalline phases of water, all known as ice, and these phases are of especial interest to astronomers and astrogeologists since many of these phases presumably exist in our solar system, e.g. in Jupiter's icy moon Europa or Saturn's moon Enceladus.

This phase diagram raises many interesting questions: how do the phases---which all consist of water molecules---differ from one another? For a given substance like water, is there a limit to how many phases can exist? What are the rules, if any, that govern how one phase changes into another phase as the temperature or pressure is varied? For example, in the figure you can see so-called triple points where three phases (such as solid, liquid, and vapor phases, or two solid phases and a liquid phase) can coexist. Can a quadruple or higher-order point exist?

We will answer some of these questions during the semester. Indeed, if we think of the different phases that form from "structureless" vapor as a kind of pattern formation (say through the formation of different crystalline structures), phase transitions become an important conceptual and technical metaphor for understanding how complex structure emerges from simpler structure as some parameter is varied. Experiments and theoretical work concerning phase transitions in fact have strongly influenced how people think about questions such as nonequilibrium pattern formation (say formation of cloud patterns or snowflakes), the transition from inanimate to animate molecules (origin of life), the formation of matter, stars, and galaxies from the superhot plasma of the Big Bang, consciousness in brains (is this an abrupt transition as brains become bigger?), and the properties of social, economic, and computer networks.

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