Unreal Nature

July 26, 2012

Whenever It Gets the Chance

Filed under: Uncategorized — unrealnature @ 7:14 am

… ‘the world can be expected to produce order whenever it gets the chance.’

This is from the end of Branches which is the third of the three book series, of Nature’s Patterns: A Tapestry in Three Parts by Philip Ball (2009):

… Most of the patterns [in Nature] that I have described appear suddenly. One moment there is nothing; then you turn the dial of the driving force up a notch, and everything is abruptly different. Stripes appear; or dunes, or pulsations. This seems to be the nature of most symmetry-breaking processes: they happen all at once. In that respect, they resemble phase transitions in equilibrium thermodynamics.

… there is a threshold that, once crossed, leaves the entire system prone to a change in state. Just the same is true for many pattern-forming processes. Convective patterns … appear above a threshold heating rate, and vortices in fluid flow above a threshold flow rate. The path of a crack goes crazy above a particular crack speed.

In addition, the change in state during an equilibrium phase transition may involve a breaking of symmetry. Crystalline ice has an ordered molecular structure (in fact it has many ordered structures), while liquid water is disorderly at the molecular scale. Again, you could be forgiven for thinking that symmetry is therefore broken during melting, but in fact it is the other way around: symmetry is broken during freezing, because whereas the liquid state is isotropic (all directions in space are equivalent) the crystal structure of ice identifies certain directions as ‘special.’

Thus equilibrium phase transitions, like the abrupt transitions that characterize much of pattern formation, are spontaneous, global, and often symmetry-breaking changes of state that happen when a threshold is crossed.

Some of these transitions involve straightforward rearrangement of one state into another. But there are classes of both equilibrium and non-equilibrium transitions that offer a choice of two alternatives for the new state, which are equivalent but not identical.. Think of the formation of convection roll cells. Adjacent rolls turn over in opposite directions, but any particular roll could rotate either one way of the other as long as all the others switch direction too. Above the convection threshold, there is a choice of two mirror-image states. Which is selected? Clearly, there is nothing to favour one over the other, and the issue is decided by pure chance. The same is true of the rotation of plughole whirlpools, unless some small outside influence tips the balance.

… The situation is like a ball perched on top of a perfectly symmetrical hill: it is unstable at the top and has to roll down one side or the other, but which way it goes is unpredictable and at the mercy of imperceptible disturbances.

[ … ]

… One of the attractive justifications of the theory of maximal entropy production is that it offers a rationalization of why ordered patterns may appear far from equilibrium. This, it is worth reminding ourselves once more, is a highly counter-intuitive phenomenon: we might expect systems driven out of equilibrium to dissolve into chaos. What is more, it appears to (although in fact does not) challenge the second law of thermodynamics, which insists that entropy and thus disorder must increase. And indeed, if we are now insisting that not only does entropy increase but it tends to do so at the maximum rate, why should there be a prescription for order rather than its opposite? The answer, according to Jaynes’s theory of entropy maximization, is that ordered states are more effective than disordered ones at producing entropy. To put it another way: suppose a system has accumulated a lot of energy and ‘needs’ to discharge it.

[line break added by me to make this easier to read online] A rather literal expression of that situation is the build-up of electrical charge in a thundercloud, which may be released by passing electrical current to the ground. One way this could happen is for the charge to hop out onto droplets of moisture or dust in the air, and for these to gradually diffuse down to the ground. That is a slow process. What often happens instead, of course, is that the charge grounds itself all at once in a lightning bolt, creating one of the branching patterns we encountered in this book. Lightning, the dielectric breakdown of air, provides a ‘structured channel’ for the release of the electrical energy at the maximal rate of entropy production. As the physicist Roderick Dewar puts it, ‘far from equilibrium, the coexistence of ordered and dissipative regions produces and exports more entropy to the environment than a purely dissipate soup.’ And so, according to Rod Swenson of the University of Connecticut ‘the world can be expected to produce order whenever it gets the chance.’

[image from Wikipedia]

Morowitz and Smith argue that the early Earth was a storehouse of energy ‘needing’ to be dissipated. In particular, there may have been plentiful hydrogen and carbon dioxide: two molecules that release energy when they react, but which do so only very slowly on their own. Primitive living organisms would have supplied a way for this to happen, ‘fixing’ carbon dioxide into organic matter through reactions that use electrons extracted from hydrogen. Similarly, some geological environments generate molecules rich in electrons and others hungry for them; but only living cells would let this transfer proceed at an appreciable rate. In other words, life may have appeared on the early Earth as a kind of lightning conductor, using order to speed up entropy production. In that picture, say Morowitz and Smith, ‘a state of the geosphere which includes life [was] more likely than a purely abiotic state.’



Blog at WordPress.com.

%d bloggers like this: