The Recurrence Paradox
The second law of thermodynamics states that energy flows from hotter to colder bodies in a way that increases the total disorder of the Universe, or equivalently, that the particles of the Universe tend to move to states that are 'more probable'. In these 'more probable' states, energy is more spread out or evenly distributed.
In a finite universe, with a finite number of particles, there is a finite, extremely small chance, for every arrangement of particles to occur. In fact, each arrangement of particles should occur twice, three times,... an infinite number of times. For purely statistical reasons, all the particles of the Universe will have exactly the same positions and velocities as they do now. It seems reasonable therefore, that history should follow the same course from now as it did the last time all the particles in the Universe have the same positions and velocities as they did then, and in fact it should follow the same course each time the particles have the same positions and velocities. History should repeat itself an infinite number of times.
The reasoning in the paragraph above conflicts with the second law of thermodynamics as discussed briefly in the first paragraph. The second law implies that energy continues to disperse, and at no stage can ever be reconstituted into any form it once had.
Which view is tue depends possibly on the fate of the Universe. If the Universe continues to expand forever, then the point of view stated in the second paragraph is implied, because energy will be distributed through the Universe, be it in an ever so diffuse form. If the Universe one day stops expanding and starts to contract eventually undergoing a 'big crunch', then possibly a recurrence of the big bang. There may be cycles of big bangs and big crunches which would imply the second point of view.