2020/10/24 by Timo J. Doerries, Doerries, Timo J., Sarah A. M. Loos +3 · 2 citations
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Material Dynamics and Properties #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2010.12806
openalex publication_date 2020/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with correlation functions of stochastic systems with\nmemory, a prominent example being a molecule or colloid moving through a\ncomplex (e.g., viscoelastic) fluid environment. Analytical investigations of\nsuch systems based on non-Markovian stochastic equations are notoriously\ndifficult. A common approximation is that of a single-exponential memory,\ncorresponding to the introduction of one auxiliary variable coupled to the\nMarkovian dynamics of the main variable. As a generalization, we here\ninvestigate a class of "toy" models with altogether three degrees of freedom,\ngiving rise to more complex forms of memory. Specifically, we consider, mainly\non an analytical basis, the under- and overdamped motion of a colloidal\nparticle coupled linearly to two auxiliary variables, where the coupling\nbetween variables can be either reciprocal or non-reciprocal. Projecting out\nthe auxiliary variables, we obtain non-Markovian Langevin equations with\nfriction kernels and colored noise, whose structure is similar to that of a\ngeneralized Langevin equation. For the present systems, however, the\nnon-Markovian equations may violate the fluctuation-dissipation relation as\nwell as detailed balance, indicating that the systems are out of equilibrium.\nWe then study systematically the connection between the coupling topology of\nthe underlying Markovian system and various autocorrelation functions.We\ndemonstrate that already two auxiliary variables can generate surprisingly\ncomplex (e.g., non-monotonic or oscillatory) memory and correlation functions.\nFinally, we show that a minimal overdamped model with two auxiliary variables\nand suitable non-reciprocal coupling yields correlation functions resembling\nthose describing hydrodynamic backflow in an optical trap.\n