Two runners step up to the starting line. One runs steadily and uses fuel sparingly. The other learns to run faster as it goes, and its fuel flares ever more fiercely. In chemistry, the competitors are a simple substance that creates itself and a molecule that copies itself from a template, the way DNA does.
The physics of nonequilibrium systems says: a pathway becomes more probable the more energy it dissipates as heat. The simple substance spends energy at a steady rate. The copying molecule, meanwhile, accelerates, and its energy expenditure grows like a double exponential, which is very fast. At first it falls behind, but then a tipping point arrives, and it pulls ahead for good.
It used to be unclear why nature selects the chemical pathways that lead to heredity. Now it is clear: copying molecules with adaptation spend energy faster than anyone else, and that is why they win. This principle can be tested in an experiment: if you measure heat release in a test tube full of chemicals, the transition to heredity will show up as a sharp rise in that heat. That is how physics explains where life comes from.
The double exponential in the probability means that after the critical moment the replicative trajectory becomes not merely more probable, but so dominant that the logarithm of its logarithm grows quadratically with time. This is one of the fastest growths encountered in physical models.