Jeremy England claims to be able explain the existence of self-replicating objects--such as life--using non-equilibrium statistical mechanics. The gist of this is that, according to the equations, a collection of atoms in a heat bath will restructure itself to dissipate more energy when in contact with an external source (such as the sun), which can be efficiently achieved by forming a self-replicator.
Such a grand claim warrants a certain amount of scepticism; indeed, not every expert is convinced. However, England is a serious scientist doing serious work--he's an Assistant Professor at MIT and recently gave a talk about this work in Oxford (one of the best talks I've seen here).
This is a very fascinating and important idea; if true, it gives a deeper scientific explanation than natural selection for the existence of life and hence further removes humankind from the centre of this cosmic drama.
"You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant."