From New Scientist:
With quantum mechanics rewritten in time-free form, combining it with general relativity seems less daunting, and a universe in which time is fundamental seems less likely. But if time doesn't exist, why do we experience it so relentlessly? Is it all an illusion?
Yes, says Rovelli, but there is a physical explanation for it. For more than a decade, he has been working with mathematician Alain Connes at the College de France in Paris to understand how a time-free reality could give rise to the appearance of time. Their idea, called the thermal time hypothesis, suggests that time emerges as a statistical effect, in the same way that temperature emerges from averaging the behaviour of large groups of molecules (Classical and Quantum Gravity, vol 11, p 2899).
Imagine gas in a box. In principle we could keep track of the position and momentum of each molecule at every instant and have total knowledge of the microscopic state of our surroundings. In this scenario, no such thing as temperature exists; instead we have an ever-changing arrangement of molecules. Keeping track of all that information is not feasible in practice, but we can average the microscopic behaviour to derive a macroscopic description. We condense all the information about the momenta of the molecules into a single measure, an average that we call temperature.
According to Connes and Rovelli, the same applies to the universe at large. There are many more constituents to keep track of: not only do we have particles of matter to deal with, we also have space itself and therefore gravity. When we average over this vast microscopic arrangement, the macroscopic feature that emerges is not temperature, but time.
More here.