Strong non-exponential relaxation and memory effects in a fluid with non-linear drag

Abstract

We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of non-linear Brownian motion, displays a really complex behaviour when quenched to low temperatures. Its glassy response is controlled by a long-lived non-equilibrium state, independent of the degree of non-linearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behaviour persists in the collisionless case, where the fluid is described by the non-linear Fokker-Planck equation. The observed response, which includes non-exponential, algebraic, relaxation and strong memory effects, presents scaling properties: the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. To account for the observed behaviour in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation -- which considers not only the fourth cumulant but also the sixth one.

18 pages, 14 figures; accepted as regular article in PRE

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• Mpemba effect in anisotropically driven inelastic Maxwell gases
• Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law
• Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag
• Mpemba effect in the relaxation of an active Brownian particle in a trap without metastable states
• Predicting the Mpemba Effect Using Machine Learning
• Mpemba effect on non-equilibrium active Markov chains
• Non-equilibrium attractor for non-linear stochastic dynamics
• Kinetic glass transition in granular gases and non-linear molecular fluids
• Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag
• Mpemba-like effect protocol for granular gases of inelastic and rough hard disks