## Research Abstracts Online

January 2010 - March 2011

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### University of Minnesota Duluth

Swenson College of Science and Engineering

Department
of Chemistry and Biochemistry

# PI: Paul D. Siders

### Dynamical Entropy of the Simple Exclusion Process

Dynamical, or "second,” entropy, defined by Phil Attard, is an entropy for a transition between two states, per time. It is hypothesized that transitions tend to maximize second entropy, as equilibrium systems tend to maximize entropy. Second entropy has been applied successfully to fluid dynamics, heat transfer, and particle flow, but not yet to any lattice models. The extremum hypothesis will be tested with a simple lattice model. To extend the definition of second entropy to lattice models, Attard’s definition in terms of phase space volumes will be interpreted in terms of the space of particle configurations. The partially asymmetric exclusion process (ASEP) in one dimension with open boundaries will be used as a test case. In the model, particles hop along a one-dimensional lattice between two reservoirs. The second entropy of transitions by which the system relaxes toward steady state will be calculated, testing whether those transitions are indeed of maximal second entropy. Motion of the ASEP through configuration space will be calculated with a master equation. A large lattice will require eigenvalues and vectors of a large but sparse rate matrix. Resources of memory and processors at MSI are essential for those calculations.

### Group Member

Carl Sandness, Faculty Collaborator