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Thermoremanent magnetization data for the three-dimensional Edwards-Anderson (EA) spin glass are generated using the waiting time method as a simulational tool and interpreted using record dynamics. We verify that clusters of contiguous spins are overturned by quakes, nonequilibrium events linked to record-sized energy fluctuations, and we show that quaking is a log-Poisson process, i.e., a Poisson process whose average depends on the logarithm of the system age, counted from the initial quench. Our findings compare favorably with experimental thermoremanent magnetization findings and with the spontaneous fluctuation dynamics of the EA model. The logarithmic growth of the size of overturned clusters is related to similar experimental results and to the growing length scale of the spin-spin spatial correlation function. The analysis buttresses the applicability of the waiting time method as a simulational tool, and of record dynamics as a coarse-graining method for aging dynamics.

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The applicability to dense hard sphere colloidal suspensions of a general coarse-graining approach called Record Dynamics (RD) is tested by extensive molecular dynamics simulations. We reproduce known results as logarithmic diffusion and the logarithmic decay of the average potential energy per particle. We provide quantitative measures for the cage size and identify the displacements of single particles corresponding to intermittent cage breakings. We then partition the system into spatial domains and show that, within each domain, a subset of such intermittent events called quakes constitutes a log-Poisson process, as predicted by RD. Specifically, quakes are shown to be statistically independent and Poisson distributed with an average depending on the logarithm of time. Finally, we discuss the nature of the dynamical barriers surmounted by quakes and link RD to the phenomenology of aging hard sphere colloids.

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We document and discuss two different modes of evolution across multiple systems, optimization and expansion. The former suffices in systems whose size and interactions do not change substantially over time, while the latter is a key property of open-ended evolution, where new players and interaction types enter the game. We first investigate systems from physics, biology, and engineering and argue that their evolutionary optimization dynamics is the cumulative effect of multiple independent events, or quakes, which are uniformly distributed on a logarithmic time scale and produce a decelerating fitness improvement when using the appropriate independent variable. The appropriate independent variable can be physical time for a disordered magnetic system, the number of generations for a bacterial system, or the number of produced units for a particular technological product. We then derive and discuss a simple microscopic theory that explains the nature of the involved optimization processes, and provide simulation results as illustration. Finally, we explore the evolution of human culture and technology, using empirical economic data as a proxy for human fitness. Assuming the overall dynamics is a combined optimization and expansion process, the two processes can be separated and quantified by superimposing the mathematical form of an optimization process on the empirical data and thereby transforming the independent variable. This variable turns out to increase faster than any exponential function of time, a property likely due to strong historical changes in the web of human interactions and to the associated increase in the amount of available knowledge. A microscopic theory for this time dependence remains, however, a challenging open problem.

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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.

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We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features astronomically large equilibration times and displays a characteristic aging behavior on all observable time scales. The density of parked cars displays quasi-equilibrium Gaussian fluctuations interspersed by increasingly rare intermittent events, quakes, which can lead to an increase of the density to new record values. Defining active clusters as the shortest domains of parked cars which must be rearranged to allow further insertions, we find that their typical length grows logarithmically with time for low enough temperatures and show how the number of active clusters on average gradually decreases as the system approaches equilibrium. We further characterize the aging process in terms of the statistics of the record-sized fluctuations in the interstitial free volume which lead to quakes and show that quakes are uncorrelated and that they can be approximately described as a Poisson process in logarithmic time.

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Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K. We first show that the interactions generated by our rule are nearly independent of K. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time t_{w} also survives at t>t_{w}. Finally, survival probabilities of species are shown to decay as powers of the ratio t/t_{w}, a so-called pure aging behavior usually seen in glassy systems of physical origin. We find a quantitative dynamical effect of trait inheritance, namely, that increasing the value of K numerically decreases the decay exponent of the species survival probability.

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We develop a simple and effective description of the dynamics of dense hard sphere colloids in the aging regime deep in the glassy phase. Our description complements the many efforts to understand the onset of jamming in low density colloids, whose dynamics is still time-homogeneous. Based on a small set of principles, our model provides emergent dynamic heterogeneity, reproduces the known results for dense hard sphere colloids and makes detailed, experimentally-testable predictions for canonical observables in glassy dynamics. In particular, we reproduce the shape of the intermediate scattering function and particle mean-square displacements for jammed colloidal systems, and we predict a growth for the peak of the χ(4) mobility correlation function that is logarithmic in waiting-time. At the same time, our model suggests a novel unified description for the irreversible aging dynamics of structural and quenched glasses based on the dynamical properties of growing clusters of highly correlated degrees of freedom.

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Monte Carlo algorithms such as the Wang-Landau algorithm and similar "entropic" methods are able to accurately sample the density of states of model systems and thereby give access to thermal equilibrium properties at any temperature. Thermal equilibrium is, however, unachievable at low temperatures in glassy systems. Such systems are characterized by a multitude of metastable configurations pictorially referred to as "valleys" of an energy landscape. Geometrical properties of the landscape, e.g., the local density of states describing the distribution in energy of the states belonging to a single valley, are key to understanding the dynamical properties of such systems. In this paper we combine the lid algorithm, a tool for landscape exploration previously applied to a range of models, with the Wang-Swendsen algorithm. To test this improved exploration tool, we consider a paradigmatic complex system, the Edwards-Anderson model in two and three spatial dimensions. We find a striking difference between the energy dependence of the local density of states in two dimensions and three dimensions--nearly linear in the first case, and nearly exponential in the second. The dynamical consequences of these findings are discussed.

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In recent experiments by Richardson et al. (2010) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2010. PLoS ONE 5, e9621.] ant motion out of the nest is shown to be a non-stationary process intriguingly similar to the dynamics encountered in physical aging of glassy systems. Specifically, exit events can be described as a Poisson process in logarithmic time, or, for short, a log-Poisson process. Nouvellet et al. (2010) [Nouvellet, P., Bacon, J.P.,Waxman, D., 2010. J. Theor. Biol. 266, 573.] criticized these conclusions and performed new experiments where the exit process could more simply be described by standard Poisson statistics. In their reply Richardson et al. (2011b) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2011b. J. Theor. Biol. 269, 356-358.] stressed that the two sets of experiments were performed under very different conditions and claimed that this was the likely source of the discrepancy. Ignoring any technical issues which are part of the above discussion, the focal point of this work is to ascertain whether or not both log-Poisson and Poisson statistics are possible in an ant society under different external conditions. To this end, a model is introduced where interacting ants move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice. The probability of each move is determined by the ensuing changes of a utility function which is a sum of pairwise interactions between ants, weighted by distance. Depending on how the interactions are defined and on a control parameter dubbed 'degree of stochasticity' (DS), the dynamics either quickly converges to a stationary state, where movements are a standard Poisson process, or may enter a non-stationary regime, where exits can be described as suggested by Richardson et al. Other aspects of the model behavior are also discussed, i.e. the time dependence of the average value of the utility function, and the statistics of spatial re-arrangements happening anywhere in the system. Finally, we discuss the role of record events and their statistics in the context of ant societies and suggest the possibility that a transition from non-stationary to stationary dynamics can be triggered experimentally.

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The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an ageing regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the ageing dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic timescale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the probability density function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters ('dynamic heterogeneity'), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is [Formula: see text], implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally, an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function.

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Linear response functions of aging systems are routinely interpreted using the scaling variable t(obs)/t(w)(mu), where t(w) is the time at which the field conjugated to the response is turned on or off, and where t(obs) is the "observation" time elapsed from the field change. The response curve obtained for different values of t(w) are usually collapsed using values of mu slightly below one, a scaling behavior generally known as subaging. Recent spin glass thermoremanent magnetization experiments have shown that the value of mu is strongly affected by the form of the initial cooling protocol [G. F. Rodriguez, Phys. Rev. Lett. 91, 037203 (2003)], and even more importantly [G. G. Kenning, Phys. Rev. Lett. 97, 057201 (2006)], that the t(w) dependence of the response curves vanishes altogether in the limit t(obs)>>t(w). The latter result shows that t(obs)/t(w)(mu) scaling of linear response data cannot be generally valid, thereby casting some doubt on the theoretical significance of the exponent mu . In this work, a common mechanism is proposed for the origin of both subaging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process.

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The fossil record has been interpreted as exhibiting a gradual decrease in the extinction rate. We use the individual based Tangled Nature model of evolutionary ecology to study the mechanisms behind this kind of nonstationary macrodynamics. We demonstrate that the long time aging in the system (manifested as a slowing down of the rate of large jumps, or quakes, that the system undergoes) is related to decreasing fluctuations in the offspring probability. The scenario is reminiscent of relaxation in a quenched spin glass but purely dynamical in nature since no energy barriers can be defined.

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At time t after an initial quench, an aging system responds to a perturbation turned on at time tw

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We numerically analyze the statistics of the heat flow between an aging system and its thermal bath, following a method proposed and tested for a spin-glass model in a recent paper [P. Sibani and H. J. Jensen, Europhys. Lett. 69, 563 (2005)]. The present system, which lacks quenched randomness, consists of Ising spins located on a cubic lattice, with each plaquette contributing to the total energy the product of the four spins located at its corners. Similarly to our previous findings, energy leaves the system in rare but large, so-called intermittent, bursts which are embedded in reversible and equilibriumlike fluctuations of zero average. The intermittent bursts, or quakes, dissipate the excess energy trapped in the initial state at a rate which falls off with the inverse of the age. This strongly heterogeneous dynamical picture is explained using the idea that quakes are triggered by energy fluctuations of record size, which occur independently within a number of thermalized domains. From the temperature dependence of the width of the reversible heat fluctuations we surmise that these domains have an exponential density of states. Finally, we show that the heat flow consists of a temperature independent term and a term with an Arrhenius temperature dependence. Microscopic dynamical and structural information can thus be extracted from numerical intermittency data. This type of analysis seems now within the reach of time resolved microcalorimetry techniques.