Giant Kovacs-Like Memory Effect for Active Particles

Abstract

Dynamical properties of self-propelled particles obeying a bounded confidence rule are investigated by means of kinetic theory and agent-based simulations. While memory effects are observed in disordered systems, we show that they also occur in active matter systems. In particular, we find that the system exhibits a giant Kovacs-like memory effect that is much larger than predicted by a generic linear theory. Based on a separation of time scales we develop a nonlinear theory to explain this effect. We apply this theory to driven granular gases and propose further applications to spin glasses.

On the emergence of large and complex memory effects in nonequilibrium fluids

“…One of the main aims of our work is to show that the actual memory effects landscape is in general far more complex than expected. First, we show that several extrema-instead of only one-may appear in a single heating/cooling protocol à la Kovacs, contrary to what has been previously observed [15][16][17][18][19][20]. Second, very large memory humps, of the order of magnitude of the stationary value of the quantity of interest, can be observed.…”

“…Two data sets from molecular dynamics (MD) simulations (see appendix B) of the granular gas for both the HP and the CP, together with their corresponding theoretical predictions, are represented in figure 2(A), which clearly shows the appearance of very large memory effects. The temperature humps displayed here, of approximately 100% for the CP and 10% for the HP, are larger by at least two orders of magnitude than previously observed memory effects in athermal systems, which at most range from a few thousandths to a few hundredths of the stationary value of the relevant variable [17,19]. The theoretical curves displayed in figure 2(A) have been obtained by means of a bi-variate Maxwellian approximation, in which all the cumulants are assumed to be zero (see appendix A).…”

“…To the best of our knowledge, both features have not yet been reported in the literature. It must be noted that humps much larger than those predicted by linear response theory have recently been found in a nonlinear active matter model [19], but the relative deviation from the steady state is still of a few hundredths therein.…”

“…We have described above the typical cooling procedure, but also a heating protocol can be considered ( < < T T T 0 s t 1 ), for which ( ) t exhibits a single minimum at t>t w . Quite recently, Kovacs-like memory effects have been thoroughly investigated in glassy systems [15,16], granular fluids [17,18], active matter [19], and Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. disordered mechanical systems [20].…”

“…disordered mechanical systems [20]. The memory effect is typically quite small: the maximum deviation of ( ) t from the stationary value  st is several orders of magnitude smaller than  st [1,15,[17][18][19].…”