3. Analysis of Generative Chemistry without Cycling and with Energy Biased Generation of Reactions.
Functional Analysis
N = 1062.
E = 3860
Density = 0.00719.
1. Degree cenrality = 2 All Degree Centralization = 0.081 Mean Degree = 7.269 Median Degree = 4.0 SD(Degree) = 8.8831.
1.1 Random Graph Degree Centrality = 3 Centralization = 0.00841 Mean Degree = 7.088 Median= 7 SD = 2.698
2. Characturistic Path Length = 3.58084 Diameter = 8.0
2.1 Random graph CPL = 3.78487, (2122 unrechable pairs). Diameter = 7.
3. Clustering Coefficient = 0.00411 SD(C) = 0.00974
3.1 Random Graph CC = 0.00306 SD(CC) = 0.00769
1. Shannon entropy. ii. Skew of the distribution. iii). kf and heat distribution.
ii). Distribution of free energies (Top right) and their relationship to steady state species concentration.(Top Left) iii). Interaction strength distribution.(Bot Right), and relationshiop to concentrations at end(Bot Left).
iv). Mean interaction strength. v). (Storage). Total Internal Free Energy of the system. vi). Energy flux.
4. Structural Properties as described before.
Conclusions
As shown below, the steady state light absorption rate is greatest at the end of the random generation run, in comparison to at the end of the run in which species with high free energy are most likely to react to produce a new reaction.
In retrospect this may have been predicted, since if the high energy species are those which are most likely to be in re-cycling loops, then causing them to engage in even more randomly generated reactions will most likely disrupt these once effective re-cycling loops, rather than benefiting them.
I was surprised at first that the biased generative regime resulted in less re-cycling. However, in retrospect this is obviously because the few short recycling loops (likely to be of high energy) experience the most side-reactions due to this bias.
If it is the case that high energy particles are more likely to undergo further reactions, i.e. their features contribute most to the exploration of the chemical space, then it is only if such an exploration can somehow achieve greater re-cycling potential that the system can circumvent the ‘Funneling catastrophe’. The metaphor of the 'funneling catastrophe' is described further in a talk given for Alife X downloadable here.
How can reaction funneling be avoided?
1. The probability of reaction must be a function not only of the energy of reactants but of reactant STRUCTURE. In particular, I predict that if high energy particles have the greatest capacity for re-configuration to obtain reaction specificity, then even if this re-configuration is random, that the system will tend towards increased steady state heat dissipation. Effectively, this may produce a Benard type instability by high energy particles doing random chemical pruning of their reactions.
2. Chemicals also have physical properties that can mediate physical specificity, e.g. by semi-permeability and diffusion limitation in a 2D or 3D space.
Given what was learned here, I can now go on and produce a third model. This model aims to include structural properties of particles that may allow them to engage in interesting shapes with defined free energies of formation and capacities for interaction that are structured. This model is developed here
The latest software used to obtain the above results is given here. It runs on XCode for Mac OS X. Help with using this code can be obtained by contacting me on ctf20@sussex.ac.uk or at C.T.Fernando@cs.bham.ac.uk
References
H.T.Odum (1975) Energy Quality and Carrying Capacity of the Earth, A response at prize awarding ceremony of Institute La Vie, Paris.
H.T.Odum (1988) 'Self-Organization, Transformity, and Information', Science, Vol. 242, pp. 1132-1139.
H.T.Odum (1994) Ecological and General Systems: An introduction to Systems Ecology, Colorado University Press, (especially page 251).
H.T.Odum (1995) 'Self-Organization and Maximum Empower', in C.A.S.Hall (ed.) Maximum Power: The Ideas and Applications of H.T.Odum, Colorado University Press, Colorado.
Lesins, G.B. (1991). Radiative entropy as a measure of complexity. In Scientists on Gaia, eds Schneider, S. & Boston, P., pp. 121±127.
American Geophysical Union.
Schneider, E.D, Kay, J.J., 1995, "Order from Disorder: The Thermodynamics of Complexity in Biology", in Michael P. Murphy, Luke A.J. O'Neill (ed), "What is Life: The Next Fifty Years. Reflections on the Future of Biology", Cambridge University Press, pp. 161-172
Ulanowicz, R. E. & Hannon, B.M. (1987). Life and the production of entropy. Proc. R. Soc. London B, 232, 181-192.