Brownian systems perturbed by mild shear: Comparing response relations

Abstract

We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.

A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics

“…The broad interest in the FDR emerged also in other areas of science ranging from equilibrium and non-equilibrium colloids [18,19], to granular particles [20][21][22], and even to biological systems, usually classified as active matter [23][24][25]. In these cases, generalized FDRs have been derived using nearequilibrium approximations [26] and have been employed to provide expressions for the transport coefficients [27], the effective temperature [28][29][30] and the effect of mild shear [31,32]. Exact relations for a colloid in an active environment have been recently investigated [33].…”