ETH Polymer Physics seminar


2003 -12 -03
10 :15 at ML J 21

Model reduction and uniqueness of thermodynamic projector

Alexander Gorban und Iliya Karlin

Institute of Polymers, ETH Zurich

We solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of thermodynamic projector is proven: There exists only one projector which transforms the arbitrary vector field equipped with the given Lyapunov function into a vector field with the same Lyapunov function for a given anzatz manifold which is not tangent to the Lyapunov function levels. Moreover,from the requirement of persistence of the sign of dissipation follows that the value of dissipation (the entropy production) persists too. The explicit construction of this thermodynamic projector is described. In example this projector is applied to derivation the equations of reduced kinetics for different systems (Boltzmann equation, Fokker-Planck equation for polymer dynamics, etc.).


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