They're adjusting the integration method (used to calculate positions given forces) to take into account the properties of the thermostat (used to maintain a roughly-constant temperature in the simulation). This allows bigger timesteps.
In particular, they studied the Langevin thermostat, in which all the atoms are subject to small random forces that smooth out their average temperature. By adding a term to the integrator that includes the magnitude of the random forces, it is possible to widen the stability bounds of the integration.
The caveat is that the proof is only for simple potential energy surfaces. They haven't given a lot of evidence, even empirically, that this works for the potential energy surfaces we really care about, like protein binding calculations. We already have many empirical tricks for increasing timesteps for these simulations, like freezing bond lengths for hydrogen. Any new method has to beat these empirical methods, not just beat a naive approach.
Yeah I've worked a lot with this and was also curious as the thermo distribution is just one part, you also have a lot of short range forces that explode if you increase the timestep by too much and I didn't see any tricks around that (except the usual like freezing the fastest degrees of freedom, completely removing hydrogens with virtual sites etc).
This is a great example of why someone else should write the high level description for somebody else's work. Without the baggage of what was hard, fun, easy, interesting (and the desire to sell/market), an outsider can focus on the importance and utility of a work.
In particular, they studied the Langevin thermostat, in which all the atoms are subject to small random forces that smooth out their average temperature. By adding a term to the integrator that includes the magnitude of the random forces, it is possible to widen the stability bounds of the integration.
The caveat is that the proof is only for simple potential energy surfaces. They haven't given a lot of evidence, even empirically, that this works for the potential energy surfaces we really care about, like protein binding calculations. We already have many empirical tricks for increasing timesteps for these simulations, like freezing bond lengths for hydrogen. Any new method has to beat these empirical methods, not just beat a naive approach.