Nonequilbrium systems comprise a large set of interesting problems across a wide range of disciplines. When systems are driven out of equilibrium by external forces that are constant or periodic in time, the system exists in a nonequilibrium steady state. This steady state is an ensemble, much like the ensembles of equilibrium statistical mechanics, except in general there does not exist a closed form of the probability of a given configuration.
Trajectories from nonequilibrium steady states can be simulated by starting in an initial configuration and propagating the system forward in time using Newton's laws. However, just as in systems in equilibrium, exploration of the space of possible configurations (phase space) is often hindered by large "free energy" barriers that separate metastable regions. To solve this problem, we have developed an enhanced sampling algorithm that divides a phase space into regions and integrates trajectory segments in each region. The method "nonequilibrium umbrella sampling", is described in Part I of this thesis to study problems in nonequilibrium systems. In each case, the method is able to promote sampling of rare events by climbing the barriers in phase space that separate high probability regions.
Although equilibrium statistical mechanics is unable to describe events in nonequilibrium systems, there have recently been advances in our ability to describe these systems analytically. Large deviation functions describe the response of a system to a biasing field that acts to exhibit uncharacteristically large deviations of the expectation value of an observable away from its average value. Discontinuities in large deviation functions, or their derivatives, reveal transitions between two dynamical behaviors of the system, and share similar properties with phase transitions in configuration space. Part II examines phase transitions of this nature. First, a driven lattice gas model with collective shear moves and friction is studied, and we observe a percolation-type phase transition between a free-flowing, low-viscosity state and a jammed, high-viscosity state. Second, we use the language of large deviation theory to describe the entrainment of an oscillator to an external driving force. We show that this entrainment is a transition between two dynamical phases.
|Advisor:||Dinner, Aaron R.|
|Commitee:||Freed, Karl F., Voth, Greg A.|
|School:||The University of Chicago|
|School Location:||United States -- Illinois|
|Source:||DAI-B 72/12, Dissertation Abstracts International|
|Subjects:||Statistics, Physical chemistry, Computer science|
|Keywords:||Dynamical phase transitions, Enhanced sampling, Large deviation functions, Nonequilibrium, Rare events, Umbrella sampling|
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