Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

Abstract

We analyze the dynamical evolution of a fluid with nonlinear 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 nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, 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 behavior 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.

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

“…As a consequence, starting from θ 0 > 1, θ(t) − 1 develops a hump with a negative minimum if a 2 (t K ) > 0; analogously, starting from θ 0 < 1, θ(t) − 1 develops a hump with a positive maximum if a 2 (t K ) < 0. Because of its formal analogy with the Kovacs effect [37,[81][82][83][84][85][86][87], we will refer to this crossover θ(t K ) = 1 and subsequent hump, either positive or negative, as a Kovacs-like phenomenon.…”

“…In a more general context, the ME can be recast as "the initially further from equilibrium relaxes faster"with the separation from equilibrium being defined in a suitable way, see below. With such an interpretation, Mpemba-like effects have been investigated in a large variety of many-body systems: molecular gases [36,37], mixtures [38], granular gases [39][40][41][42][43][44], inertial suspensions [45,46], spin glasses [47], carbon nanotube resonators [48], clathrate hydrates [49], Markovian models [50][51][52][53][54], active systems [55], Ising models [56,57], non-Markovian mean-field systems [58,59], or quantum systems [60]. Also, it has been experimentally observed in colloids [61,62].…”

“…There have been two main approaches to the ME: the kinetic-theory or "thermal" approach [36][37][38][39][40][41][42][43][44][45][46] and the stochastic-process (or thermodynamics) or "entropic" approach [50][51][52][53][54][55][60][61][62]. In the thermal approach, kinetic theory makes it possible to define in a natural way an out-of-equilibrium time-dependent temperature T (t) (basically, the average kinetic energy).…”

“…Let us consider the following model for a fluid with nonlinear drag [36,37,[66][67][68]: a d-dimensional fluid of elastic hard spheres of mass m and diameter σ, with number density n, subjected to a stochastic force composed by a white-noise term with nonlinear variance plus a nonlinear drag force. This scheme mimics a system of elastic spheres assumed to be suspended in a background fluid in equilibrium at temperature T b .…”

“…A quadratic dependence of the drag coefficient naturally appears when the hard spheres and the background fluid particles have a comparable mass [36,37,[66][67][68],…”