From: jlg@cochiti.lanl.gov (Jim Giles)
Subject: Re: sci.skeptic FAQ version 0.2.
Organization: Los Alamos National Laboratory
Date: Wed, 26 Aug 1992 18:08:29 GMT

In article <1928@snap>, paj@uk.co.gec-mrc (Paul Johnson) writes:

A lot of stuff.  I'll just remark on one point that's actually scientifically
inaccurate.

|> [...]
|> 5.6: "The second law of thermodynamics says....
|> -----------------------------------------------
|> 
|> ...that entropy is always increasing.  Entropy is a measure of the
|> randomness in a system.  So the universe is getting more and more
|> disordered.  But if this is so, how can life happen, since
|> evolutionists claim essentially that life is a system that becomes
|> more ordered with time?"

The Clausius statement of the second law of thermodynamics:

      No process is possible whose *sole* result is a heat flow out
      of one system at a given temperature and a flow of heat into
      a second system at a higher temperature.

In other words, it takes power to run your refrigerator - there will
never be any that run for free.

The Kelvin-Plank statement the second law of thermodynamics:

      No process is possible whose *sole* result is a heat flow out of
      a system and at a given temperature and the performance of work
      with that energy.

In other words, you can't get work except by exploiting a temperature
gradient (at least, not thermodynamically - forms of potential energy
other than heat may be used - but they can also be used to make a
heat gradient).

Notice that neither statement of the second law even mentions the word
"disorder".  In fact, the principle of entropy increase also does not,
since entropy is a thermodynamic state variable whose definition is
independent of such ill-defined terms as "disorder".

So, where does this idea that entropy is a measure of "disorder" come
from - and what does it mean anyway?  Well, the idea comes from a
mistatement of the theory of statistical mechanics.  And the meaning
is nil - since the term "disorder" has no precise scientific meaning
anyway.

In statistical mechanics, "entropy" is defined in terms of the number
of distince energy "microstates" that are possible within the system.
At any given time, the system will be in *one* of those states - but
"entropy" is defined as a formula (actually the log of a sum) based 
on the number (and relative probabilities) of such states which are 
available (that is, those which don't violate conservation laws or 
the assumptions of the statistical model).  It turns out that if you
have a physical system in which the component parts obey the statistical
model you choose, the actual thermodynamic entropy differs from the
statistical measure of entropy only by a constant multiple (Boltzman's
constant).

Now, this diversity of states was (and sometimes still is) informally
called "disorder" by some statistical mechanics experts when trying
to convey a feel for the subject to lay audiences.  It was never a
technical term - and never had any specific meaning in the theory.

Now, the term "disorder" applied in this way is misleading (or, at
best, meaningless).  A room which is messy would be informally called
"disordered" by most people - even if they're ignorant (as most are)
of the entropy of the room.  The room might actually have *lower*
entropy that it does after you clean it!  In fact, cleaning is a 
quite energetic process, so I'm willing to bet on it.

On the other hand, the analogy between entropy and evolution is still
interesting ( though analogies are *never* the same as *evidence*).
Statistical mechanical entropy requires the diversity of systems
increase (or remain unchanged), and mutation causes the diversity
of genetic traits to increase (by a process to which the information
theoretic version of entropy - a mathematically similar concept - really
*is* applicable). 

By the way, biologists *don't* claim that life is a process that gets 
more ordered with time.  They claim that mutation causes diversity to
increase, and that selection pressures (often caused by abrupt changes
in isolated populations, rather than gradual effects) winnow this 
diversity back down - so that the number and nature of species changes 
with time.  There is nothing `counter-thermodynamic' going on here.

-- 
J. Giles