Umbrella Sampling for Non-Equilibrium Processes

Thursday, July 26, 2007 - 4:10pm - 4:30pm
EE/CS 3-180
Aaron Dinner (University of Chicago)
Many systems of significant fundamental and applied interest are irreversible.
These include, but are not limited to, living systems, chemical reactors,
systems with driven flows of matter and energy, and photoactivated systems. For theoretical studies of such non-equilibrium processes, the steady-state
distribution is of central importance because it enables calculation of static
averages of observables for comparison to experimental measurements. For
systems at equilibrium, low probability states can be explored efficiently in
simulations with umbrella sampling methods, in which biasing potentials that
are functions of one or more order parameters are used to enhance sampling of
selected regions of phase space. What complicates extending umbrella sampling
to simulations of non-equilibrium processes is that, by definition, they do not
obey detailed balance (microscopic reversibility). As such, one must account
for the fact that the steady-state probability of observing particular values
of the order parameters can be determined by a balance of flows in phase space
through different possible transitions. In this talk, I will describe the
first algorithm for enforcing equal sampling of different regions of phase
space in an ergodic system arbitrarily far from equilibrium, which enables its
steady-state probability distribution to be determined with high accuracy. The
efficiency of the algorithm will be demonstrated by applying it to a model of a
genetic toggle switch which evolves irreversibly according to a continuous time
Monte Carlo procedure.