Wednesday, January 23, 2013

Mmm... pancakes...

A scientist's aim in a discussion with his colleagues is not to persuade, but to clarify. (Leo Szilard)

I have always wished I had the opportunity to 'Order out of Chao's'
I've just finished reading "Order out of Chaos: Man's New Dialogue with Nature" by Nobel Laurate Ilya Prigogine and Isabelle Stengers. Wary as I am of criticising a Nobel Laureate, I have to say I was disappointed with it.  

The first few chapters, on the history of science, were most enjoyable, and I appreciated the clarity Prigogine and Stengers brought to the distinction between traditional physics as the science of reversible processes and chemistry as the science of irreversible processes. (I should declare my bias here at the outset. By training and inclination I regard reversible processes as no more than useful mathematical fictions. All real processes are irreversible. Hier steh ich.)

I began to have serious misgivings in Chapter IV, where free energy is introduced.  Gibbs’ conception of free energy is a powerful tool for understanding the universe because it combines that which is seen and that which is not seen: the entropy change in the system and the entropy change in the surroundings, the rest of the universe.  In “Order out of Chaos”, free energy is introduced merely as a function used to define equilibrium in closed systems, without describing its fundamental link to entropy, and its usefulness in understanding the formation of dissipative structures is explicitly (and incorrectly) denied in subsequent chapters.

The discussion of oscillating reactions in Chapter V is obfuscatory in referring to ‘products’ what should strictly be called ‘intermediates’, and in neglecting to state not only that the overall driving force of the reaction A --> E is the free energy change in the system, but that the direction of each of the intermediate steps at each point in time is determined by the free energy change.  By focussing on the chimeric idea of achieving maxima in thermodynamic functions – something only valid at equilibrium – and ignoring the paramount importance of changes in these functions (all we ever talk about in chemistry!) the authors draw a veil of muddle over exciting and interesting phenomena. They claim that ‘the concept of probability that underlies Boltzmann’s order principle is no longer valid in that the structures we observe do not correspond to a maximum of complexions’, but this is only true if a myopic focus is made on the system, rather than the surroundings.  The complex oscillations – and dissipative structures in general – come about because they are the most efficient means, given the history of the system, to increase the entropy (the number of complexions) of the surroundings.  Structure does not arise spontaneously within the system: it is propagated from the interface between the system and the surroundings.  This is more clearly seen in the physical system of the BĂ©nard cell which is also discussed in Chapter V, but it is equally true for chemical systems.  The confusion that arises from blurring the distinction between system and surroundings continues throughout the book.

Chapter VI suffers from an overabundance of metaphors drawn from diverse fields of study that serve to obscure whatever fundamental point the authors are trying to make.  In between a discussion of how termite mounds are formed and a brief discussion of homogeneous nucleation of phase changes, they state: “although Boltzmann’s order principle enables us to describe chemical or biological processes in which differences are levelled out and initial conditions forgotten, it cannot explain situations such as these, where a few ‘decisions’ in an unstable situation may channel a system formed by a large number of interactive entities toward a global structure”.  It is not true that Boltzmann’s order principle only enables us to describe chemical or biological processes in which differences are levelled out: a global structure will spontaneously form in any number of situations, such as micellisation of a surface active agent, driven by an increase in the entropy in the unstructured component of the system fully explicable by Boltzmann’s order principle.  In the real world, homogeneous nucleation of structure is relatively rare. Physical and chemical transformations to give structure are nucleated heterogeneously – from the surroundings, and as order propagates inward from interfaces very different effects can be seen: it is true that Boltzmann’s principle cannot tell us a priori which structure will form, whether homogeneously or heterogeneously nucleated, but this does not mean structure formation per se is in any way incompatible with it. 

Not being terribly familiar with Prigogine previously, I had expected that Stuart Kauffman’s wild concept of ‘order for free’ was based on a misreading of Prigogine’s work, but all the ingredients for it are here, alas...:(