They say that every molecule has a will of its own. They also say that we are defined by the choices we make, and that each choice leads to a different and predetermined outcome. Similar to the Chaos Theory, one choice by an individual molecule will lead to something far more grand, that in our limited scope we cannot fathom. To bring this stretch onto a farther level, they say that there is an alternate dimension for each possible choice that a molecule could make, and then the varying ripples of its outcome. From the moment before an action is committed towards the aftereffect, it is gleaned that we are not the same... the world is altered, through its billions of people pushing and pulling.
The idea of rebirth in terms of Theravadic Buddhism is that we are constantly becoming reborn. In the very similar stance that the paragraph beforehand mentioned, there is no single and universal similarity to the actions we take and our conditions in the before and after. With the idea that each molecule has its own consciousness and will, our outcomes are always vast in possibility. Through the lens of this viewpoint, consciousness and will can be viewed as sequences.
Against our premonitions, Theravadic Buddhism does not view consciousness as a continuum, and as the paragraph stated before - things are better described in series of interlaced events. Rebirth is not merely the incarnation of the soul into another body nor the beginning of a new cycle as the mythological phoenix has shown us. Instead, it is the death and birth of the mind. As humans, our thoughts and desires are temporal and are constantly shifting. When shifting, they are being birthed or falling into death. One example is that we do not consistently feel lust; we feel it and when it is sated, such a state of consciousness dies while a new one is born. Perhaps the consciousness and desire to eat?
Through each state of our minds, we garner different perceptions and feelings. The mindset we have is merely for the moment (however long it may be), and dies when the moment is over. Thus, rising from those proverbial ashes, is a new mindset based on a new instance.