A fairly old idea put forth by a number of philosophies and religions that suggests that the contents of the universe undergo an endless series of cycles, and therefore the universe's state at any given moment will ultimately recur again. And again. And so on.

Henri PoincarĂ© kind of proved that, if the universe were to last for an infinite amount of time, a kind of eternal recurrence would indeed take place. As a physicist of note because he developed and mathematically confirmed using newtonian physics that, given essentially an inifinite amount of time, the particles in a closed system would reform to their state at any given point. This means that, for example, if you had a liter of air and placed it in a box where nothing could get in or out, the air would ultimately reform to the way it was at any given time. Likewise, the universe (if it were a closed system) could ultimately reform to the way it was at any given time, meaning that nothing we do means anything since we are caught up in endless, repeating cycles. However, for this to actually be applicable, virtually an infinite amount of time would be required.

The formula determining the amount of required time, according to Poincare, is like 10 raised to the power of the number of atoms in the system... A liter of plain air has a trillion trillion particles, so it would take 10^trillion trillion seconds to reform. The universe itself is only like 10^17 seconds old, so it is basically an inifinite amount of time. In response to this idea of eternal recurrence, Friedrich Nietzsche uttered his famous words, "God is dead."

But the universe isn't exactly a closed mechinical system, so this may not happen after all.

Of course, this isn't overly interesting: consider a deck of cards. Record its configuration at this very moment. Then randomly shuffle it, examining its configuration after each shuffle. Ultimately, if you do this for an infinite amount of time, it will, of course, return to its former configuration.

Still, it's pretty cool.