Fluctuating viscoelasticity based on a finite number of dumbbells
Abstract
Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.02797
- arXiv:
- arXiv:2011.02797
- Bibcode:
- 2020arXiv201102797H
- Keywords:
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- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Statistical Mechanics;
- Physics - Chemical Physics;
- Physics - Computational Physics
- E-Print:
- 14 pages, 1 figure