Eternal return (also known as "eternal recurrence") is a concept which posits that the universe has been recurring, and will continue to recur in a self-similar form an infinite number of times. The concept has roots in ancient Egypt, and was subsequently taken up by the Pythagoreans and Stoics. With the decline of antiquity and the spread of Christianity, the concept fell into disuse, though Friedrich Nietzsche resurrected it on the grounds that it provides a reason for affirming life after the decline of theism.
In addition, the philosophical concept of eternal recurrence was addressed by Arthur Schopenhauer. It is a purely physical concept, involving no "reincarnation", but the return of beings in the same bodies. Time is viewed as being not linear but cyclical.
The basic premise is that the universe is limited in extent and contains a finite amount of matter, while time is viewed as being infinite. The universe has no starting or ending state, while the matter comprising it is constantly changing its state. The number of possible changes is finite, and so sooner or later the same state will recur.