"A simulation of a physical process on a computer cannot use the exact, continuous equations of motion; the calculations must use approximations over discrete intervals of time," says Sivak. "It's well known that standard algorithms that use discrete time steps don't conserve energy exactly in these calculations."
One workhorse method for modeling molecular systems is Langevin dynamics, based on equations first developed by the French physicist Paul Langevin over a century ago to model Brownian motion. Brownian motion is the random movement of particles in a fluid (originally pollen grains on water) as they collide with the fluid's molecules particle paths resembling a "drunkard's walk," which Albert Einstein had used just a few years earlier to establish the reality of atoms and molecules. Instead of impractical-to-calculate velocity, momentum, and acceleration for every molecule in the fluid, Langevin's method substituted an effective friction to damp the motion of the particle, plus a series of random jolts.
When Sivak and his colleagues used Langevin dynamics to model the behavior of molecular machines, they saw significant differences between what their exact theories predicted and what their simulations produced. They tried to come up with a physical picture of what it would take to produce these wrong answers.
"It was as if extra work were being done to push our molecules around," Sivak says. "In the real world, this would be a driven physical process, but it existed only in the simulation, so we called it 'shadow work.' It took exactly the form of a nonequilibrium driving force."
They first tested this insight with "toy" models havi
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DOE/Lawrence Berkeley National Laboratory