Ned Wright is a cosmologist who has some wonderful pages on cosmology, including a

FAQ which answers this very question:

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Does entropy prevent a Big Crunch?

The issue of entropy in the Universe is subtle and not entirely settled. Theorists are still trying to work out what happens to the entropy of matter that falls into a black hole, a problem which involves both quantum mechanics and strong gravity. When a successful theory of quantum gravity is worked out, it should explain why the Universe came out of the Big Bang singularity with a very large entropy, and what happens to the entropy of the Universe if it recollapses.

Entropy is related to the number of ways a system can be in a given state or condition. Thus a shuffled deck of cards has a higher entropy than a new deck with all the suits in order. Adding energy to a system usually opens up more states, and increases the entropy. The temperature of a system is defined such that kT is the amount of energy needed to increase the number of available states by a factor of e = 2.71828... where k is Boltzmann's constant. Transferring heat from a hot piece of a system to a cold piece increases the number of ways to arrange the cold part by a larger factor than the decrease in the number of ways to arrange the hot piece. Thus the normal flow of heat from hot to cold causes an increase in the number of ways the whole system can be arranged which is then an increase in the total entropy of the whole system.

Entropy need not always increase in open systems. Energy could be used to make entropy decrease for a particular system. Your refrigerator does this by removing heat from the interior, if you consider the interior of your refrigerator to be a separate system. Of course, if you consider both the internal and external portions of the refrigerator then there is a net increase of entropy due to the inefficiency of the refrigerator.

Since entropy is a statistical concept, short term fluctuations in small systems can allow entropy to decrease.

Entropy remains constant in a system with a uniform temperature that has no heat added or subtracted from it. This is thought to be more or less the case for the Universe or for any representative piece of the Universe that expands or contracts in the same way the Universe does. The vast majority of the entropy of the Universe is in the cosmic microwave background radiation because the vast majority of particles in the Universe are the photons of the CMB. As the Universe expands, the temperature of the radiation drops to maintain constant entropy. If the Universe were to collapse at some point, the radiation would heat back up to maintain constant entropy. When the Universe expanded the radiation started out in thermal equilibrium with the matter and then de-coupled. In the collapse the radiation and the matter would once again come into thermal equilibrium. Whatever happened with the dynamics of the matter in the interim would be reflected in the final thermal equilibrium with the radiation. The final entropy of the Universe as it approaches the Big Crunch singularity would be larger than the initial entropy of the Universe because of the heat added by nuclear fusion in stars, so a recollapse does not involve a decrease in entropy.