Title: Comparative Analysis of Fluctuations in Viscoelastic Stress: A Comparison of the Temporary Network and Dumbbell models

Abstract: Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as noise, hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped, as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the dumbbell model. Despite both models conforming to the Upper Convected Maxwell Model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure-flow coupling, beyond what is captured by macroscopically averaged stresses.