FIRTH%TARTAN@CMU-CS-C.ARPA (05/22/84)
In my opinion, the best discussion of the controversy concerning the
Second law of Thermdynamics is contained in
Natural Philosophy of Cause and Chance - Max Born
(Dover pb). If you are interested, go read the book. If you are interested
enough to put up with an overbrief summary, one follows.
First, there is no such law in a Newtonian universe. The analysis of this
problem by the Ehrenfests has suffered no serious challenge, and it shows
(a) The motion of Newtonian particles is fully reversible; that is, there
is no "arrow of time"
(b) the theorems of Laplace and Zermelo, that a collection of Newtonian
particles will eventually return arbitrary closely to its initial
configuration (provided it has negative total energy), are valid.
(c) the proofs of the "law" are circular. In particular, the H-theorem,
which is the statistical-mechanical foundation of the law, can be
proved only by fudging the collision integral to contain an assumption
of intrinsic randomness. This proves that a collection of ordered
particles, subjected to random forces, will become disordered. That
is not quite good enough.
Secondly, while there is a direction of time in most quantum theories,
there is not an absolute second law either. In particular, there are
objects that cannot be brought into thermal equilibrium with their
surroundings, and so adiabatic transformations cannot generally be made
on such objects. Most "proofs" of increasing entropy in fact prove
that quantum systems are "more likely" to evolve towards more disordered
states. This unfortunately does not prove that there is a secular
increase in entropy, since the unlikely events may correspond to very
large changes. As an analogy, a sawtooth curve slopes downhill "almost"
everywhere, but its average height remains the same.
It would be too much of a digression to discuss those cosmological
theories that predict violations of the FIRST law of thermodynamics.
Robert Firth
PS: "What one man is able to imagine, other men will be able to do"
(Jules Verne)
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