
The Question
(Submitted December 23, 1996)
Correct me if I'm wrong, but the 2nd law of thermodynamics states that
Entropy
i.e. the disorder in the Universe, must increase with time.
Does this mean that a closed Universe will violate the 2nd law of
thermodynamics ?
Or, would a better definition of entropy be  Increase in the
homogeneity of the
energy/mass distribution of the Universe.
If this alternative definition is adopted then a closed Universe would
not violate
the 2nd law of thermodynamics.
I could of course be entirely wrong , but I would be interested in your
comments.
The Answer
I asked Demos Kazanas, a theorist the Astrophysics Science Division,
to take a look at your question. I attach his response.
Paul Butterworth
Imagine the Universe!
The issue of entropy in gravitating systems is indeed one issue which has
not yet been resolved satisfactorily. Let me see if I get your train
of thought: you think that a closed Universe, by requiring all matter
in it to revert to a state of contraction would violate the second law
because we learn from gases that they generally tend to expand if
given the volume? If this is indeed your argument, it is not totally
correct, as it is based on the notions of entropy developed from the
study of noninteracting gases. Once interactions become important,
then while entropy may still represent disorder, that notion of disorder
is different from that obtained by looking at a noninteracting gas.
You can think of the intricate snowflake patterns as such an example.
Their formation represents a higher entropy situation for the given
conditions of temperature and density and yet they are not disordered at
all. The difference comes about because of the intermolecular interactions.
Gravity acts in a similar fashion. The difference is that these
interactions are long range and affect the evolution of the gas at all
times and not only when the temperature becomes small enough. So the
recontraction of the Universe does not decrease its entropy; it takes place
precisely because of the action of the gravitational force. In fact the
evolution of the Universe is totally adiabatic, as far as the matter
content is concerned (if one assumes that it remains homogeneous and
isotropic) since the gravitational field does work on the gas to contract
it and heat it up . Now, Penrose has argued that that as far as the
gravitational field is concerned, homogeneity and isotropy are very
unlikely conditions. The gravitational field wants matter to be clumped
and therefore, as you have guessed, as the Universe progresses (whether it
recontracts or not) it should become increasingly inhomogeneous (which is
of course observed). In the recontracting phase these inhomogeneities
get greatly amplified and would push the entire matter of the Universe
into a large number of black holes, i.e. the collapse will be very
inhomogeneous. This inhomogeneity provides a great increase in
gravitational entropy, much more than that one gets by the (possible)
decrease due to the compression of the gas. So the second law remains
valid. I hope this answers your question.
