Behaviour intermediate between Stable & Unstable Equilibrium
| This is a game of random walk. This time we cast a coin in stead of a dice. If a tail is obtained, we replace an arbitrary black piece by a white piece; If we obtain a head, the replacement is reversed. The uncertainty of an elementary event may have a direct bearing on the macroscopic distribution. The system will oscillate randomly between the two extreme cases (all pieces are either black or white) |
| The difference between the 3 games is
demonstrated by the probability values for the extreme cases indicated. The
occupation of the board exclusively by black or white pieces in random walk
requires on an average 32 generations ( 322 = about 1000 throws) if the
initial distribution was uniform. In the second game, such a state is
attained only after 1 generation (64 throws ). In the 1st game i.e. Ehrenfest game, for an extreme state to be attained, about 1019 throws are
needed, since the probability of such a state is ( 1/2)-64 .i.e. 10-19. In all these games, there are no conditions for selection: metabolism, self-reproduction ( autocatalysis) and mutations. |
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The key problem being solved by the Eigen model theory is the problem of the emergence of an ordered structure from the original chaos, the problem of creation of information. As we have seen, the appearance of order ,its selection and maintenance are possible in an open autocatalytic template system that is far from equilibrium. The theory admits self organization which was contradictory to the thoughts of physicists like Wigner who concluded that pre-biotic self -organization is impossible and contradicted the basic laws of physics. |