arXiv subjects

Paolo Sibani

Publications and source records attributed to Paolo Sibani.

At least 19 recordsLinked to original sources

arXiv2022

Human wealth evolution is an accelerating expansion underpinned by a decelerating optimization process

Optimization and expansion are two modes of staged evolution of complex systems where macroscopic observables change at a decreasing, respectively increasing, rate. A prime example of evolutionary expansion, Gross Domestic Product (GDP) time series gauge economic activities in changing societal structures,} and the accelerating trend of their growth probably reflects a manyfold increase of the human interactions that drive change. We show how optimization and expansion can coexist by replacing `wall clock time' $t$ as independent variable with a measure of human interactions intensity $τ$. Our analysis of eight centuries of yearly GDP data from three regions of Western Europe is carried out in two steps. First, a Monte Carlo algorithm is used to fit the GDP data to a piecewise continuous function comprising a sequence of exponentials with different exponents. In a second step, GDP data are plotted vs. $τ$ and shown to display two logarithmic regimes, both decelerating, that are joined by a power-law cross-over period. We connect the end of the first regime and the beginning of the second with the dawn of the Industrial Revolution and the societal impact of new transport, communication and production technologies that became widely available after World War I. We conclude that wealth evolution in terms of $τ$ is a decelerating process with the hallmarks of record dynamics optimization.

physics.soc-ph↗

arXiv2021

Extremal fluctuations driving the relaxation in glassy energy landscapes

Cooperative events requiring anomalously large fluctuations are a defining characteristic for the onset of glassy relaxation across many materials. The importance of such intermittent events has been noted in systems as diverse as superconductors, metallic glasses, gels, colloids, and granular piles. Here, we show that prohibiting the attainment of new record-high energy fluctuations -- by explicitly imposing a ``lid'' on the fluctuation spectrum -- impedes further relaxation in the glassy phase. This lid allows us to directly measure the impact of record events on the evolving system in extensive simulations of aging in such vastly distinct glass formers as spin glasses and tapped granular piles. Interpreting our results in terms of a dynamics of records succeeds in explaining the ubiquity of both, the logarithmic decay of the energy and the memory effects encoded in the scaling of two-time correlation functions of aging systems.

cond-mat.soft↗

arXiv2020

Record dynamics of evolving metastable systems: theory and applications

Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as "physical aging", but from the vantage point of RD the evolution of a class of systems of physical, biological and cultural origin is rooted in a hierarchically structured configuration space and can therefore be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showinghe basic RD hypothesis, the log time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RG could be of use.

cond-mat.stat-mech↗

arXiv2020

Spin-glass thermo-remanent magnetization revisited: a numerical and analytical study

Thermoremanent magnetization data for the 3D Edwards-Anderson spin glass are generated using the Waiting Time Method as simulational tool and interpreted using Record Dynamics. We verify that clusters of contiguous spins are overturned by quakes, non-equilibrium events linked to record sized energy fluctuations and 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 results compare favorably with experimental thermoremanent magnetization findings and with the spontaneous fluctuation dynamics of the E-A model. The logarithm 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 coarse-graining method for aging dynamics.

cond-mat.stat-mech↗

arXiv2020

Human wealth evolution: trends and fluctuations

Is a causal description of human wealth history conceivable? To investigate the matter we introduce a simple causal albeit strongly aggregated model, assuming that the observed wealth growth is mainly driven by human collaborative efforts whose intensity itself increases with increasing wealth. As an empirical reference we use time series describing eight centuries of per capita annual gross domestic products (GDP) of three European countries, the UK, France and Sweden. The model requires a population large enough for disruptive events, e.g. famine, epidemics and wars, not to destroy the fundamental workings of society. The wealth evolution trend can then be described by an ordinary differential equation with three free parameters. The solution features a finite time singularity, which suggests a lack of long term sustainability. The year at which the singularity occurs has a slight variation near 2020 AD from one country to another. GDP time series curtailed after 1900 AD produce similar values for the occurrence of the singularity, which thus could be predicted more than hundred years ago. Curtailing the GDP series from the early years up to 1700 AD also produces stable and consistent predictions for the singularity time. {Power spectra are obtained for de-trended data spanning eight centuries, as well as for the first and last four centuries of the same period. All spectra have an overall signature where the power decays as the inverse frequency squared. The embedded peaks are reminiscent of the cycles described in the economic literature, but are also present in time series far predating industrialization. The background fluctuations in the GDP series is tentatively interpreted as societal response to disruptive stochastic events. e.g. new economic activities following epochal discoveries, as well as wars and epidemics

nlin.AO↗

arXiv2019

Dynamics of dense hard sphere colloidal systems: a numerical analysis

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 cage breakings. We then partition the system into spatial domains. Within each domain, a subset of intermittent events called quakes is shown to constitute a log-Poisson process, as predicted by Record Dynamics. Specifically, these events 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.

cond-mat.stat-mech↗

arXiv2018

Aging is a log-Poisson Process, not a Renewal Process

Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a non-equilibrium, 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 like 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 (RD) provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.

cond-mat.soft↗

arXiv2018

Mesoscopic real space structures in aging spin-glasses: the Edwards-Anderson model

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below $T_{\rm c}$ and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures $T$ can be collapsed by scaling them with $T^{1.75}$, a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the cluster, as recently assumed in a coarse grained model of dense colloidal dynamics. The evolving structure of clusters in real space is finally sssociated to the decay of the thermo-remanent magnetization. Our analysis provides an unconventional coarse-grained description of spin glass aging as statistically subordinated to a Poisson quaking process and highlights record dynamics as a viable common theoretical framework for aging in different systems.

cond-mat.stat-mech↗

arXiv2016

Record Dynamics: Direct Experimental Evidence from Jammed Colloids

In a broad class of complex materials a quench leads to a multi-scaled relaxation process known as aging. To explain its commonality and the astounding insensitivity to most microscopic details, record dynamics (RD) posits that a small set of increasingly rare and irreversible events, so called quakes, controls the dynamics. While key predictions of RD are known to concur with a number of experimental and simulational results, its basic assumption on the nature of quake statistics has proven extremely difficult to verify experimentally. The careful distinction of rare ("record") cage-breaking events from in-cage rattle accomplished in previous experiments on jammed colloids, enables us to extract the first direct experimental evidence for the fundamental hypothesis of RD that the rate of quakes decelerates with the inverse of the system age. The resulting description shows the predicted growth of the particle mean square displacement and of a mesoscopic lengthscale with the logarithm of time.

cond-mat.soft↗

arXiv2016

Decision Making on Fitness Landscapes

We discuss fitness landscapes and how they can be modified to account for co-evolution. We are interested in using the landscape as a way to model rational decision making in a toy economic system. We develop a model very similar to the Tangled Nature Model of Christensen et. al. that we call the Tangled Decision Model. This is a natural setting for our discussion of co-evolutionary fitness landscapes. We use a Monte Carlo step to simulate decision making and investigate two different decision making procedures.

q-bio.PE↗

arXiv2016

Cultural Evolution as a Non-Stationary Stochastic Process

We present an individual based model of cultural evolution, where interacting agents are coded by binary strings standing for strategies for action, blueprints for products or attitudes and beliefs. The model is patterned on an established model of biological evolution, the Tangled Nature Model (TNM), where a `tangle' of interactions between agents determines their reproductive success. In addition, our agents also have the ability to copy part of each other's strategy, a feature inspired by the Axelrod model of cultural diversity. Unlike the latter, but similarly to the TNM, the model dynamics goes through a series of metastable stages of increasing length, each characterized by mutually enforcing cultural patterns. These patterns are abruptly replaced by other patterns characteristic of the next metastable period. We analyze the time dependence of the population and diversity in the system, show how different cultures are formed and merge, and how their survival probability lacks, in the model, a finite average life-time. Finally, we use historical data on the number of car manufacturers after the introduction of the automobile to the market, to argue that ourmodel can qualitatively reproduce the flurry of cultural activity which follows a disruptive innovation.

physics.soc-ph↗

arXiv2016

Record Dynamics in the Parking Lot Model

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 re-arranged 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.

cond-mat.soft↗

arXiv2016

The Tangled Nature Model of evolutionary dynamics reconsidered: structural and dynamical effects of trait inheritance

The Tangled Nature Model of biological and cultural evolution features interacting agents which compete for limited resources and reproduce in an error prone fashion and at a rate depending on the `tangle' of interactions they maintain with others. The set of interactions linking a TNM individual to others is key to its reproductive success and arguably constitutes its most important property. Yet, in many studies, the interactions of an individual and those of its mutated off-spring are unrelated, a rather unrealistic feature corresponding to a point mutation turning a giraffe into an elephant. To bring out the structural and dynamical effects of trait inheritance , we introduce and numerically analyze a family of TNM models where a positive integer $K$ parametrises correlations between the interactions of an agent and those of its mutated offspring. For $K=1$ a single point mutation randomizes all the interactions, while increasing $K$ up to the length of the genome ensures an increasing level of trait inheritance. We show that the distribution of the interactions generated by our rule is nearly independent of the value of $K$. Changing $K$ strengthens the core structure of the ecology, leads to population abundance distributions which are better approximated by log-normal probability densities and increases the probability that a species extant at time $t_{\rm w}$ is also extant at a later time $t$. In particular, survival probabilities are shown to decay as powers of the ratio $t/t_{\rm w}$, similarity to the pure aging behaviour approximately describing glassy systems of physical origin. Increasing the value of $K$ decreases the numerical value of the decay exponent of the power law, which is a clear quantitative dynamical effect of trait inheritance.

q-bio.PE↗

arXiv2014

Evolution and non-equilibrium physics. A study of the Tangled Nature Model

We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of the Tangled Nature Model (TNM) of biological evolution to show that punctuated equilibria successively generated by the model's dynamics have increasing entropy and are separated by increasing entropic barriers. We further show that these states are organized in a hierarchy and that limiting the values of possible interactions to a finite interval leads to stationary fluctuations within a component of the latter. A coarse-grained description based on the temporal statistics of quakes, the events leading from one component of the hierarchy to the next, accounts for the logarithmic growth of the population and the decaying rate of change of macroscopic variables. Finally, we question the role of fitness in large scale evolution models and speculate on the possible evolutionary role of rejuvenation and memory effects.

q-bio.PE↗

arXiv2014

Temporal and spatial heterogeneity in aging colloids: a mesoscopic model

A coarse-grained model of dense hard sphere colloids building on simple notions of particle mobility and spatial coherence is presented and shown to reproduce results of experiments and simulations for key quantities such as the intermediate scattering function, the particle mean-square displacement and the $χ_{4}$ mobility correlation function. All results are explained by two emerging and interrelated dynamical properties: i) a rate of intermittent events, quakes, which decreases as the inverse of the system age t; ii) a length scale characterizing correlated domains, which increases linearly in log t. This leads to simple and accurate scaling forms expressed in terms of a single scaling variable Finally, we propose a method to experimentally extract the growing length scale of an aging colloid and suggest that a suitable scaling of the probability density function of particle displacement can experimentally reveal the rate of quakes.

cond-mat.soft↗

arXiv2013

Coarse-graining complex dynamics: Continuous Time Random Walks vs. Record Dynamics

Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical of complex dynamics is provided by a fat-tailed distribution of the waiting time between consecutive jumps. We first argue that CTRW are inadequate to describe macroscopic relaxation processes for three reasons: macroscopic variables are not self-averaging, memory effects require an all-knowing observer,and different mechanisms whereby the jumps affect macroscopic variables all produce identical long time relaxation behaviors. Hence, CTRW shed no light on the link between microscopic and macroscopic dynamics. We then highlight how a more recent approach, Record Dynamics (RD) provides a viable alternative, based on a very different set of physical ideas: while CTRW make use of a renewal process involving identical traps of infinite size, RD embodies a dynamical entrenchment into a hierarchy of traps which are finite in size and possess different degrees of meta-stability. We show in particular how RD produces the stretched exponential, power-law and logarithmic relaxation behaviors ubiquitous in complex dynamics, together with the sub-diffusive time dependence of the Mean Square Displacement characteristic of single particles moving in a complex environment.

cond-mat.stat-mech↗

arXiv2013

Optimization by Record Dynamics

Large dynamical changes in thermalizing glassy systems are triggered by trajectories crossing record sized barriers, a behavior revealing the presence of a hierarchical structure in configuration space. The observation is here turned into a novel local search optimization algorithm dubbed Record Dynamics Optimization, or RDO. RDO uses the Metropolis rule to accept or reject candidate solutions depending on the value of a parameter akin to the temperature, and minimizes the cost function of the problem at hand through cycles where its `temperature' is raised and subsequently decreased in order to expediently generate record high (and low) values of the cost function. Below, RDO is introduced and then tested by searching the ground state of the Edwards-Anderson spin-glass model, in two and three spatial dimensions. A popular and highly efficient optimization algorithm, Parallel Tempering (PT) is applied to the same problem as a benchmark. RDO and PT turn out to produce solution of similar quality for similar numerical effort, but RDO is simpler to program and additionally yields geometrical information on the system's configuration space which is of interest in many applications. In particular, the effectiveness of RDO strongly indicates the presence of the above mentioned hierarchically organized configuration space, with metastable regions indexed by the cost (or energy) of the transition states connecting them.

cond-mat.stat-mech↗

arXiv2011

Entropic algorithms and the lid method as exploration tools for complex landscapes

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 not achievable 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 understand 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-Andersom model in two and three spatial dimension. We find a striking difference between the energy dependence of the local density of states in the two cases: nearly flat in the first case, and nearly exponential in the second. The lid dependence of the data is analyzed to estimate the form of the global density of states.

cond-mat.stat-mech↗