hypnagogue said:
Royce, please give http://www.2ndlaw.com/ a thorough reading. Pay particular attention to the sections "The second law of thermodynamics is a tendency" and "Obstructions to the second law make life possible."
They've got it backwards. The life is a shortcut to maximum entropy[/color]. Consider an experiment with two identical perfectly closed rooms, except that one has a live cat, another a dead cat. Which room will have a higher entropy in a year?
This is mathematically similar to a phenomenon with a data compression -- any algorithm which compresses some data patterns will on everage produce the net data expansion over all possible data patterns.
Consider for example data collection where any item can have only 8 discrete values (uniformly distributed over the collection, e.g. a set of 8 eight distinct items). The flat, non-compressed code would encode the items 1-8 as 3-bit strings, for example as:
1. 000
2. 001
3. 010
4. 011
5. 100
6. 101
7. 110
8. 111
Suppose you decide to compress the item 1 code from 000 to 00 (i.e. you wish to lower the information entropy of item 1 by one bit; analogous to lowering the entropy of a live creature). In order for the compressed item 1 to be distingushable from the old item 2, which had a code 001, you now need a different 2-bit prefix for the item 2 (the only symbols you have are 0 and 1, i.e. you have no commas or spaces to distinguish 00 from 001 on that basis). But since all other 2-bit prefixes (01,10,11) are fully used up, you need to extend two other codes[/color] by one bit, e.g. you can code items 2 and 3 as 0100 and 0101, yielding the net expansion of 1 bit for the (information) entropy of the whole system of all eight items.
Similarly, if you wished to reduce the entropy of the item 1 by two bits, coding it as 0, then the items 2,3,4 would need longer codes since prefix 0 is now fully used up, requiring expansion of three additional codes by 1 bit (e.g. items 5,6 and 7 would gain an extra bit and share their 3 bit prefixes with the expanded codes for items 2,3 and 4), yielding the entropy expansion of 6 bits for the rest of the system (the new total size would be 1*1+6*4+1*3=28 bits vs the old size of 8*3=24 bits), i.e. now you pay the 2 bit saving on the item 1 by a 6-bit cost on the rest of the system, resulting in the net entropy increase for the whole system of 4 bits. For a system of n=2^s items, if one item is reduced maximally (from s bits to 1 bit i.e. reduced by s-1 bits), the overall system entropy grows by 2^s-s-1 bits. Or more generally, if the entropy of one item is reduced by r bits, where r<s, then the overall entropy grows by 2^(r+1)-r-2 bits.
The same mathematics (Kraft's inequality and its generalizations) which leads to the larger net information entropy operates for the physical entropy (which is also a log(NumberOfDistinctStates), except with a different convention for the unit multiplier) -- if there is a mechanism/process which creates an imbalance by making some sub-system (such as a live organism) maintain a lower entropy you always pay an interest in excess entropy for the whole system which is exponential in the amount of "saving" on the low entropy sub-system.
Life is thus an exponential accelerator of the entropy growth, an extremely efficient shortcut to the thermal equilibrium (max entropy) or in the terminology of that article, the life is the enhancer of the 2nd law, not the obstruction.