Core References for Non-Equilibrium Theory, and Initial Discussion on Financial Meltdown of 2008-2009, Lehman Brothers, Examples of Webposts Increasing over Time

Gathering up two of the most classic sources:

Prigogine’s Thermodynamics of Irreversible Processes , and Kubicek and Marek’s Computational Methods in Bifurcation Theory and Dissipative Structures.

So here’s an interesting little do-at-home experiment: Study the meltdown of the Lehman Brothers, which started the whole stock market runoff in September / October of 2008. Using Google (which is a horrible tool for this, but freely available), run queries on “Lehman Brothers” and maybe a key phrase such as “financial crisis” for each of a set of days over the summer — if you want to short-cut, just try months, such as June, 2008; then replace that with July, 2008, then August, 2008, etc.

Month Total query returns (using Google)

April, 2008: 241.000 hits
May, 2008: 1,120,000 hits:
June, 2008: 324,000 hits.
July, 2008: 408,000 hits
August, 2008: 377,000 hits
September, 2008: 769;,000 hits (Lehman files for bankruptcy)
October, 2008: 844,000 hits

Now Google’s page-rank algorithm is the quirkiest thing in the world — results change ALL THE TIME when you use it. So when you run this little mini-experiment, you’ll get different results from me. (I could run it 10 minutes from now and get different results.)

The point is — despite the HUGE amount of noise in the return sets (using such a crude means for date stamping — any data collection lab could do much better), we see that the Lehman Brothers criticality did not “happen overnight.” There was MUCH discussion about Lehman Bros. for months prior to the decision to file for bankruptcy.

Even given that such corporate crises take a long time to brew, and then to come to a simmer, something pushed the whole situation over the edge. (And not just the Lehman Bros. filing.) This situation was unstable for a long time before it broke.

If we were to pick a physical systems analogy to describe what happened, we could say that the entire financial structure was in a “stationary non-equilibrium state,” using a term coined by Prigogine.

(Note that one of Sutter’s key bones of contention with Beinhocker’s Origins (see Sutter’s review on Amazon’s Origins page) is that Beinhocker pays homage to the Complex Adaptive Systems (CAS) work at the Santa Fe Institute (SFI), while carefully ignoring the equally — and perhaps much more important — work by Prigogine and others of the European school.

(My personal take is that Prigogine’s work deals much more thoughtfully with the core issues of developing a robust model for non-equilibrium systems, and the CAS work, by and large, is much more “phenomenalistic” — they have lots of cool algorithms, lots of neat little demos, but not much that can really provide a robust and rigorous model. Still somewhat TBD, and over the course of this blog, I’ll undoubtedly have much more to say.)

So the point to ponder, quoting Prigogine w/r/t “stationary non-equilibrium states” (p. 75) is that:

“No confusion should arise between such states and equilbirum states which are characterized by zero entropy production. Another example of a stationary state is afforded by a system which receives a component M from the outside environment and transforms it through a certain number of intermediate compounds into a final product F which is returned to the external environment. A stationary state arises when the concentrations of the intermediate components no longer vary with time.”

So … with Lehman Bros., with the entire economic superstructure that existed prior to the October meltdown — can we identify components M and F, along with intermediate compounds? If we can, we might be able to make the analogy —
— this will take some pondering.

And if anyone wants to post a comment, go ahead.

In the meantime — reading Prigogine and jumping ahead a couple of pages (pg. 85); w/r/t/ Eqn. (6.44):
The entropy flow then becomes:
d(e)S/dt = Sum(over gamma) {s(sub-gamma) (dn(e)n(gamma)/dt)}

(am going to learn how to cut and paste equation images into this …)

“The inequality (6.38) for the stationary state leads to the conclusion that the entropy of the matter entering the system has to be smaller than the entropy of the matter given off by the system to the external world . From the thermodynamic point of view the open system ‘degrades’ the matter it receives and it is this degradation which maintains the stationary state.”

So — were Lehman Bros. and others “giving off more entropy” than the material (e.g., investment funds) that they received originally contained? In short, did they produce greater — not so much randomness (too simplistic a term) but rather distribution over possible states?

Another point to ponder …