Variational principles in renormalization theory

Variational Principles in Renormalization Theory

The variational principles introduced by Kadanoff et al in the renormahzatmn theory are analyzed. It is shown that the values for the specific heat critical exponent a which can be found by a variational method are restricted to a < 0 or t~ = 1 (first order transition). The reason is the confluence of the singularities in the free energy and in the variational parameters. A full implementation ...

Variational Principles in the Linear Dynamic Theory of Viscoelasticity

Statistical mechanical theory for steady state systems. VI. Variational principles.

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principle...

New variational principles with applications to optimization theory and algorithms

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Perturbation theory for critical points of causal variational principles

The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a diffeomorphism. Then the constructions are extended to convex combinations of such measures, leading to perturbation expansions for the mean and the fluctuatio...