But while it's easy to see where thermalization leads (to tepid coffee and eventual heat death), it's less obvious how the process begins. "If you start far from equilibrium, like in the early universe, how does the arrow of time emerge, starting from first principles?" said Jürgen Berges, a theoretical physicist at Heidelberg University in Germany who has studied this problem for more than a decade.

Over the last few years, Berges and a network of colleagues have uncovered a surprising answer. The researchers have discovered simple, so-called "universal" laws governing the initial stages of change in a variety of systems consisting of many particles that are far from thermal equilibrium. Their calculations indicate that these systems--examples include the hottest plasma ever produced on Earth and the coldest gas, and perhaps also the field of energy that theoretically filled the universe in its first split second--begin to evolve in time in a way described by the same handful of universal numbers, no matter what the systems consist of.

The findings suggest that the initial stages of thermalization play out in a way that's very different from what comes later. In particular, far-from-equilibrium systems exhibit fractal-like behavior, which means they look very much the same at different spatial and temporal scales. Their properties are shifted only by a so-called "scaling exponent"--and scientists are discovering that these exponents are often simple numbers like ½ and -⅓. For example, particles' speeds at one instant can be rescaled, according to the scaling exponent, to give the distribution of speeds at any time later or earlier. All kinds of quantum systems in various extreme starting conditions seem to fall into this fractal-like pattern, exhibiting universal scaling for a period of time before transitioning to standard thermalization.

"I find this work exciting because it pulls out a unifying principle that we can use to understand large classes of far-from-equilibrium systems," said Nicole Yunger Halpern, a quantum physicist at Harvard University who is not involved in the work. "These studies offer hope that we can describe even these very messy, complicated systems with simple patterns."