Phase Transition

The universal cosmic process was not created by any god or man; it forever was, is, and forever will be, an Ever living Fire.

Heraclitus

Although the formulas weren't yet written, the ancients already had an abductive sense of this fundamental motif of creation. Earth, Fire, Water and Air, these are none other than the phases we know as Solid, Plasma, Liquid and Gas. It was perceived millennia before humanity developed the mathematical language of physics that describes it precisely.

The Ising Model

When a ferromagnet is heated above its Curie temperature, it demagnetizes. The Ising model is a formalization of this process. Above the Critical Point, the micro state magnetic poles are fluctuating and in the macro state, they don't align on net. Below the critical point, the poles can freeze into a coherent average direction and the macro behavior is of a familiar magnet.

A related formalization is the Ising Problem, where the coupled poles are arranged on an arbitrary graph, rather than a lattice. Researchers have created solutions for this using non-linear optical Wave Computer, which could shine light on the nature of 00 stubs/Consciousness.

The Ising model is useful for exploring the intuition, but in everyday life we more often find condensed matter phases transitions. For example in H2O, as it changes from ice to water to steam.

Unfolding through time

The mathematics of freezing can be found in cosmological evolution.

10^22 K and above: frontier of knowledge
10^22 K: Strong force and electro-weak force separate
10^15 K: electro-weak force separates into electromagnetic force and the weak force
**10^13 K: ** A transition with the internal fields of the strong force, leading to the spatial configurations of atomic nuclei, e.g. the proton and neutron.
10^12 K: A condensation transition wherein the nuclei combine into elements.
10^5 K: Electrons condense from plasma to form neutral atomic elements with nuclei.
5000 K: Atoms condense to form molecules and with that, the combinatorial diversity of chemical bonding is
Condensed matter forms the familiar phases of gas, liquid and solid. On the earth we find a dizzying menagerie of matter states and configuration, the electronic phenomena of conductance, sound waves and at very cold temperatures super conductance.
Notice that in a liquid there are one type of wave: pressure; but in a solid, there are pressure and shear waves.

Thus, the undifferentiated blaze of the early universe breaks its symmetries and cools into the kaleidoscopic combinatorial mega-diversity of this living world. [1]

The Order Parameter

In the example of ferromagnetism above, the order parameter of net magnetism would be chosen. It is zero above the critical point and transitions to a non-zero value below that point as the poles align.

A striking claim is made in The Origin and Nature of Life on Earth, that in the non-equilibrium soup of deep ocean vents a phase transition occurred wherein flux through the rTCA chemical auto-catalytic loop ought to be chosen as the order parameter for the biosphere as a phase of matter.

Glass, Jamming and Long distance correlations

The dynamics of glasses is one of the the oldest and most challenging in the theory of matter. [2] Unlike, the depicted grid for the ising model above, in glasses long range correlations arise. As in this animation of a granular funnel flow, jamming couples distant grains.

imgs%2Fapp%2Fcollective-intel%2FkQAXnOB7SN.gif?alt=media&token=c3192f64-bc62-44c0-8ba9-6409b6f66c6c

When cooling a glass past its glass transition temperature, the molecular vibrations reach a point where there isn't sufficient gaps for them to fit though. The glass forms in a frustrated configuration, with greater trapped potential energy if it is cooled rapidly. On the macro level, it will creep through its state space. Just as an old window pane can be seen to flow over decades. On the meso level, this creep will evolve as punctuated equilibrium dynamics where cascades redistributes the frustrations to dissipate trapped potential energy.

This mode of evolution through a coupled energy landscape is relevant to Complexity in individuals and ecosystems. The codeword that defines species or ecological assemblage slowly churns in an analogous way. Here multiple levels can coevolve, as in the Cambrian explosion, where changing ecosystem architectures correspond to changes in low-level developmental regulatory networks. [4]

imgs%2Fapp%2Fcollective-intel%2FRTjLGnBxGA.webp?alt=media&token=f04f51d8-9bd1-4d26-978c-e0f4f850fc16

footnotes