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A. Vulpiani

Publications and source records attributed to A. Vulpiani.

At least 19 recordsLinked to original sources
arXiv2019

On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems

We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperperturbed dynamics. In these relations, typically one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in non-standard cases, including driven granular media, systems with a multiscale structure, active matter and systems showing anomalous diffusion.

cond-mat.stat-mech↗
arXiv2018

Anomalous mobility of a driven active particle in a steady laminar flow

We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale $\tau_A$. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ($\tau_A=0$) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite $\tau_A$ a more complex force-velocity relation can be observed.

cond-mat.stat-mech↗
arXiv2018

Langevin equation in systems with also negative temperatures

We discuss how to derive a Langevin equation (LE) in non standard systems, i.e. when the kinetic part of the Hamiltonian is not the usual quadratic function. This generalization allows to consider also cases with negative absolute temperature. We first give some phenomenological arguments suggesting the shape of the viscous drift, replacing the usual linear viscous damping, and its relation with the diffusion coefficient modulating the white noise term. As a second step, we implement a procedure to reconstruct the drift and the diffusion term of the LE from the time-series of the momentum of a heavy particle embedded in a large Hamiltonian system. The results of our reconstruction are in good agreement with the phenomenological arguments. Applying the method to systems with negative temperature, we can observe that also in this case there is a suitable Langevin equation, obtained with a precise protocol, able to reproduce in a proper way the statistical features of the slow variables. In other words, even in this context, systems with negative temperature do not show any pathology.

cond-mat.stat-mech↗
arXiv2017

Temperature in and out of equilibrium: a review of concepts, tools and attempts

We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short historical survey of the key role of temperature in thermodynamics and statistical mechanics, we tackle a series of issues which have been recently reconsidered. In particular, we discuss different definitions and their relevance for energy fluctuations. The interest in such a topic has been triggered by the recent observation of negative temperatures in condensed matter experiments. Moreover, the ability to manipulate systems at the micro and nano-scale urges to understand and clarify some aspects related to the statistical properties of small systems (as the issue of temperature's "fluctuations"). We also discuss the notion of temperature in a dynamical context, within the theory of linear response for Hamiltonian systems at equilibrium and stochastic models with detailed balance, and the generalised fluctuation-response relations, which provide a hint for an extension of the definition of temperature in far-from-equilibrium systems. To conclude we consider non-Hamiltonian systems, such as granular materials, turbulence and active matter, where a general theoretical framework is still lacking.

cond-mat.stat-mech↗
arXiv2017

About thermometers and temperature

We discuss a class of mechanical models of thermometers and their minimal requirements to determine the temperature for systems out of the common scope of thermometry. In particular we consider: 1) anharmonic chains with long time of thermalization, such as the Fermi-Pasta-Ulam (FPU) model; 2) systems with long-range interactions where the equivalence of ensembles does not always hold; 3) systems featuring absolute negative temperatures. We show that for all the three classes of systems a mechanical thermometer model can be designed: a temporal average of a suitable mechanical observable of the thermometer is sufficient to get an estimate of the system's temperature. Several interesting lessons are learnt from our numerical study: 1) the long thermalization times in FPU-like systems do not affect the thermometer, which is not coupled to normal modes but to a group of microscopic degrees of freedom; 2) a thermometer coupled to a long-range system measures its microcanonical temperature, even at values of the total energy where its canonical temperature would be very different; 3) a thermometer to read absolute negative temperatures must have a bounded total energy (as the system), otherwise it heavily perturbs the system changing the sign of its temperature. Our study shows that in order to work in a correct way also in "non standard" cases, the proper model of thermometer must have a special functional form, e.g. the kinetic part cannot be quadratic.

cond-mat.stat-mech↗
arXiv2017

Anomalous force-velocity relation of driven inertial tracers in steady laminar flows

We study the nonlinear response to an external force of an inertial tracer advected by a two-dimensional incompressible laminar flow and subject to thermal noise. In addition to the driving external field $F$, the main parameters in the system are the noise amplitude $D_0$ and the characteristic Stokes time $\tau$ of the tracer. The relation velocity vs force shows interesting effects, such as negative differential mobility (NDM), namely a non-monotonic behavior of the tracer velocity as a function of the applied force, and absolute negative mobility (ANM), i.e. a net motion against the bias. By extensive numerical simulations, we investigate the phase chart in the parameter space of the model, $(\tau,D_0)$, identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.

cond-mat.stat-mech↗
arXiv2016

Nonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility

We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force which induce the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of non-equilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.

cond-mat.stat-mech↗
arXiv2014

Scaling properties of field-induced superdiffusion in Continous Time Random Walks

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.

cond-mat.stat-mech↗
arXiv2014

Fluctuations in partitioning systems with few degrees of freedom

We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, at varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation which cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical timescale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.

cond-mat.stat-mech↗
arXiv2012

Rare events and scaling properties in field-induced anomalous dynamics

We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.

cond-mat.dis-nn↗
arXiv2012

Reaction Spreading on Graphs

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, M(t). At variance with pure diffusive processes, characterized by the spectral dimension, d_s, for reaction spreading the important quantity is found to be the connectivity dimension, d_l. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t) ~ t^{d_l}. In the case of Erdos-Renyi random graphs, the reaction-product is characterized by an exponential growth M(t) ~ e^{a t} with a proportional to ln , where is the average degree of the graph.

cond-mat.stat-mech↗
arXiv2012

The prediction of future from the past: an old problem from a modern perspective

The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability results to be hindered rather by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, regardless the regular or chaotic nature of the system, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.

nlin.CD↗
arXiv2011

Estimate of temperature and its uncertainty in small systems

The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the reservoir. From such a perspective the temperature has an uncertainty, which can be treated within the framework of estimation theory. We review the main results of this theory, and clarify some controversial issues regarding temperature fluctuations. We also offer a simple example of a thermometer with a small number of particles. We discuss the relevance of the total observation time, which must be much longer than the decorrelation time.

cond-mat.stat-mech↗
arXiv2010

Entropy production and coarse-graining in Markov processes

We study the large time fluctuations of entropy production in Markov processes. In particular, we consider the effect of a coarse-graining procedure which decimates {\em fast states} with respect to a given time threshold. Our results provide strong evidence that entropy production is not directly affected by this decimation, provided that it does not entirely remove loops carrying a net probability current. After the study of some examples of random walks on simple graphs, we apply our analysis to a network model for the kinesin cycle, which is an important biomolecular motor. A tentative general theory of these facts, based on Schnakenberg's network theory, is proposed.

cond-mat.stat-mech↗
arXiv2009

The fluctuation-dissipation relation: how does one compare correlation functions and responses?

We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR, can be more insightful than a definition of ``non-equilibrium'' or ``effective temperatures''.

cond-mat.stat-mech↗
arXiv2008

Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file

We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $ \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation (FD) relation, i.e. the proportionality between the response function and the correlation function, when the gas is elastic or diluted. On the contrary, in strongly inelastic or dense cases, when the tracer velocity is no more independent of the other degrees of freedom, the Einstein formula fails and must be replaced by a more general FD relation.

cond-mat.stat-mech↗
arXiv2008

Twenty-five years of multifractals in fully developed turbulence: a tribute to Giovanni Paladin

The paper {\it On the multifractal nature of fully developed turbulence and chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984 (vol {\bf 17}, page 3521) has been a starting point of many investigations on the different faces of selfsimilarity and intermittency in turbulent phenomena. Since then, the multifractal model has become a useful tool for the study of small scale turbulence, in particular for detailed predictions of different Eulerian and Lagrangian statistical properties. In the occasion of the 50-th birthday of our unforgettable friend and colleague Giovanni Paladin (1958-1996), we review here the basic concepts and some applications of the multifractal model for turbulence.

nlin.CD↗