# 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.

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.