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.

Graphical abstract

中文翻译：

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基于有限数量的哑铃的波动粘弹性

摘要。

根据有限数量的哑铃的动力学，采用两种替代途径得出具有波动的构象张量的粘弹性。第一条路线仅是使用随机演算的直接方法，它是第二条路线的基准，第二条路线受热力学原理指导。在后者中，亥姆霍兹自由能和广义松弛张量起关键作用。结果表明，只有考虑到对构象张量的亥姆霍兹自由能的有限大小贡献，两条路径的结果才会一致。利用统计机制，本文为一类大型模型明确推导了这种有限大小的贡献。只要观察体积中的哑铃数量有限，此贡献就不会为零。

图形概要