Aging is a log-Poisson process, not a renewal process

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Aging is a log-Poisson process, not a renewal process

Stefan Boettcher, Dominic M. Robe, and Paolo Sibani

Phys. Rev. E 98, 020602(R) – Published 20 August 2018

Abstract

Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium “fluid” state into a nonequilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process such as CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations (“quakes”). We show that such a record dynamics provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.

Received 21 March 2018

DOI:https://doi.org/10.1103/PhysRevE.98.020602

Physics Subject Headings (PhySH)

Aging Jamming

Colloids Glasses Spin glasses

Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Stefan Boettcher¹, Dominic M. Robe¹, and Paolo Sibani²

¹Department of Physics, Emory University, Atlanta, Georgia 30322, USA
²Institut for Fysik Kemi og Farmaci, Syddansk Universitet, DK-5230 Odense M, Denmark

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Issue

Vol. 98, Iss. 2 — August 2018

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Images

Figure 1
Accumulated number of relaxation events (“quakes”) with time $t$ after a quench during simulations of (a) a continuous-time random walk (CTRW), (b) a jammed 2D colloid, and (c) a 3D Edwards-Anderson spin glass. In (a), we sampled the number of escapes by evolving Eq. (2) for a rather small value of $α = 0.1$ , to more closely resemble the physical aging data in (b) and (c). In (b) we measured intermittent cage breaks after a quench, marked by irreversible neighborhood swaps in the molecular-dynamics simulations. Also shown are the data from the colloidal experiment by Yunker et al. [10, 21]. In (c), we obtained the irreversible barrier crossings in a 3D Edwards-Anderson spin glass. Note that the physical data are growing logarithmically with time, while such a behavior is obtained in the CTRW only for $α \to 0$ .
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Figure 2
Poisson statistics of (a) the CTRW in Eqs. (1) and (2) for $α = 0.1$ , and for the aging dynamics in simulations of (b) a colloid and (c) a spin glass. Times $t_{k}$ mark the $k th$ event, i.e., escaping a trap in the CTRW, an irreversible cage break in a colloid, or quakes in a spin glass. The CTRW does not have the exponential form expected for a Poisson process, while both physical aging processes do. Generally, when too many events (i.e., too many degrees of freedom) are blurred together, it hides the local impact of the decelerating activated events and tails weaken. Record dynamics predicts that the rate of events is proportional to the number $n$ of degrees of freedom observed. As the inset for both (b) and (c) shows, the data in the aging simulations indeed collapse when rescaled by $n$ .
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Figure 3
Energy trace during a single aging process in a 3D EA spin-glass system with time $t$ after a quench. The energy decreases logarithmically with time in a widely fluctuating manner. Unlike in a renewal process, a glass never returns to energy levels visited decades earlier, signifying the gradual but significant structural evolution in the configuration of spins. Energy leaves the systems in intermittent and irreversible escape events (“quakes”) out of “valleys” (yellow arrows) triggered by a record fluctuation (red arrows). Inset: Tumbling through a complex energy landscape, a time sequence of lowest-energy (E) and highest-barrier (B) records (relative to the most recent “E”) is produced [39, 40]. Only the highest and lowest records of the “E and “B” are kept to give a strictly alternating sequence “EBEBE....” Then, any “BEB” sequence demarcates entering and escaping a valley. As in-cage rattle within a colloid, each valley represents a local metastable domain in the landscape where the system exhibits quasiequilibrium behavior on timescales shorter than the escape time.
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Figure 4
Log-Poisson statistics for the cluster model [25] on a square lattice of size $L = 200$ . Inset: Data collapse when rescaled by $n$ , as in Figs. 2 and 2 for colloid and spin glass.
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