Linear response subordination to intermittent energy release in off-equilibrium aging dynamics

The interpretation of experimental and numerical data describing off-equilibrium aging dynamics crucially depends on the connection between spontaneous and induced fluctuations. The hypothesis that linear response fluctuations are statistically subordinated to irreversible outbursts of energy, so-called quakes, leads to predictions for averages and fluctuations spectra of physical observables in reasonable agreement with experimental results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using simulational data from a simple but representative Ising model with plaquette interactions, direct statistical evidence supporting the hypothesis is presented and discussed in this work. A strict temporal correlation between quakes and intermittent magnetization fluctuations is demonstrated. The external magnetic field is shown to bias the pre-existent intermittent tails of the magnetic fluctuation distribution, with little or no effect on the Gaussian part of the latter. Its impact on energy fluctuations is shown to be negligible. Linear response is thus controlled by the quakes and inherits their temporal statistics. These findings provide a theoretical basis for analyzing intermittent linear response data from aging system in the same way as thermal energy fluctuations, which are far more difficult to measure.Comment: 9 pages, 10 figures. Text improve

Evolution and extinction dynamics in rugged fitness landscapes

Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also study the effect of externally added `mass' extinctions. The predictions for various quantities of paleontological interest (life-time distributions, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data. Brief version of parts of this work have been published as Letters. (PRL 75, 2055, (1995) and PRL, 79, 1413, (1997))Comment: 30 pages 9 figures LaTe

How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts

The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium glassy dynamics recently introduced by the authors. Invoking the concept of marginal stability, this theory links irreversible `intermittent' events, or `quakes' to thermal fluctuations of record magnitude. The pivotal idea is that the largest energy barrier $b(t_w,T)$ surmounted prior to $t_w$ by thermal fluctuations at temperature $T$ determines the rate $r_q \propto 1/t_w$ of the intermittent events occurring near $t_w$. The idea leads to a rate of intermittent events after a negative temperature shift given by $r_q \propto 1/t_w^{eff}$, where the `effective age' $t_w^{eff} \geq t_w$ has an algebraic dependence on $t_w$, whose exponent contains the temperatures before and after the shift. The analytical expression is verified by numerical simulations. Marginal stability suggests that a positive temperature shift $T \to T'$ could erase the memory of the barrier $b(t_w,T)$. The simulations show that the barrier $b(t_w,T') \geq b(t_w,T)$ controls the intermittent dynamics, whose rate is hence $r_q \propto 1/t_w$. Additional `rejuvenation' effects are also identified in the intermittency data for shifts of both signs.Comment: Revised introduction and discussion. Final version to appear in Journal of Statistical Mechanics: Theory and Experimen

Aging and intermittency in a p-spin model of a glass

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 Letter (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 equilibrium-like 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 micro-calorimetry techniques.Comment: 9 pages, 6 figures, europhysics letter style, to appear in Physical Review

A soluble model of evolution and extinction dynamics in a rugged fitness landscape

We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly we analytically derive the $t^{-2}$ law which characterizes the life time distribution of biological genera. Thirdly we discuss other dynamical properties of the model such as the rate of extinction and conclude with a brief discussion.Comment: 6 pages LaTeX source with 2 figures. Submitted to PRL (Jan. 97

Properties of the energy landscape of network models for covalent glasses

We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration space regions enclosing deep-lying energy minima. We extract the local densities of states and of minima, and the number of states and minima accessible below a certain energy barrier, the 'lid'. These quantities show on average a close to exponential growth as a function of their respective arguments. We calculate the configurational entropy for these pockets of states and find that the excess specific heat exhibits a peak at a critical temperature associated with the exponential growth in the local density of states, a feature of the specific heat also observed in real glasses at the glass transition.Comment: RevTeX, 19 pages, 7 figure

Mean-field theory of temperature cycling experiments in spin-glasses

We study analytically the effect of temperature cyclings in mean-field spin-glasses. In accordance with real experiments, we obtain a strong reinitialization of the dynamics on decreasing the temperature combined with memory effects when the original high temperature is restored. The same calculation applied to mean-field models of structural glasses shows no such reinitialization, again in accordance with experiments. In this context, we derive some relations between experimentally accessible quantities and propose new experimental protocols. Finally, we briefly discuss the effect of field cyclings during isothermal aging.Comment: Some misprints corrected, references updated, final version to apper in PR

Evolution on a Rugged Landscape:Pinning and Aging

Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank equation which allows us to describe the dynamics of the population in terms of thermo-activated Langevin diffusion of a single particle in a specific random potential. We found that the randomness in the mutation rate leads to pinning of the population and on average to a logarithmic slowdown of the evolution, resembling aging phenomenon in spin glass systems. In contrast, the randomness in the replication rate turns out to be irrelevant for evolution in the long-time limit as it is smoothed out by increasing ``evolution temperature''. The analytic results are in a good agreement with numerical simulations.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let