 03475 Alexander N. Gorban, Iliya V. Karlin
 Uniqueness of thermodynamic projector and kinetic basis of molecular individualism
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Oct 26, 03

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Abstract. Two results are presented: First, 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 {\it sign} of dissipation follows that the {\it value} of
dissipation (the entropy production) persists too. The explicit construction of this {\it
thermodynamic projector} is described. In example we apply this projector to derivation the equations
of reduced kinetics for the FokkerPlanck equation. This equation describes the polymer dynamics in
flow. The new class of closures is developed: The kinetic multipeak polyhedrons. Distributions of
this type are expected to appear in each kinetic model with multidimensional instability as
universally, as Gaussian distribution appears for stable systems. The number of possible relatively
stable states of polymer molecules grows as $2^m$, and the number of macroscopic parameters is in
order $mn$, where $n$ is the dimension of configuration space, and $m$ is the number of independent
unstable directions in this space. The elaborated class of closures and equations pretends to
describe the effects of ``molecular individualism". This is the second result.
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