Entropy ~ Probability
Now the opposite of probability is the inverse or 1/Probability = Improbability so we may say if a state of matter moves to a more improbable state it represents a drop in entropy.But entropy is also a measure of 'disorder' or loss in complexity so we may write..
Complexity ~ - Entropy (negative entropy)
And so by inference..Complexity ~ Improbability
But the above implies that (- entropy) ~ (1/entropy) which is not true mathematically! But there is a math function for which negation of the function equals the function of the inverse! Logarithm. Hense the equation for entropy [s = k logW] and for a change in entropy from s1 to s2 we haves2 – s1 = k log W2 - k log W1 = k log W2/W1
So 's' is a measure of complexity and related to probability by the log function of the probability called W. Hense the second law is expressed as in some engineering texts:“The second law of thermodynamics means that any system of paritcles, left to itself, will tend to move to its most probable state”.
Tendancy means it is the average outcome of a large number of events, usually referred to as a 'statistically significant' number. This is true for everything made of atoms! It includes chemical reactions as well as physical pressures, temperatures and even nuclear reactions. It encompasses all imaginable states of matter regardless of size from electrons to elephants and giardia to galaxies.
So any propositon or theory that claims to result in an average increase in complexity like evolution by natural selection, can be tested by the above for compliance with the second law. If it fails that test it is falsified regardless of the amount of data interpreted in its favour, that interpretation must be incorrect.
Have a nice day..
Absolutly amazing!
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