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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 non-interacting 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 non-interacting 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.

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