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Unusual statistics for extended systems

Stefano Isola, Stefano Ruffo
1991 Journal de Physique II  
doi:10.1051/jp2:1991144 fatcat:6qcwyo6b6zdhlew7dm47vzdwfi

Thermodynamics of nonadditive systems [article]

Ivan Latella, Agustín Pérez-Madrid, Alessandro Campa, Lapo Casetti, Stefano Ruffo
2015 arXiv   pre-print
The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the constituents. We present here an approach in which nonadditive systems can be described within a purely thermodynamics formalism. The basic concept is to consider a large ensemble of replicas of the system where the standard formulation of thermodynamics can be
more » ... urally applied and the properties of a single system can be consequently inferred. After presenting the approach, we show its implementation in systems where the interaction decays as 1/r^α in the interparticle distance r, with α smaller than the embedding dimension d, and in the Thirring model for gravitational systems.
arXiv:1505.03767v1 fatcat:ojivb6ub3betrp3h6xjbsadaya

Phase transitions in the unconstrained ensemble [article]

Alessandro Campa, Lapo Casetti, Ivan Latella, Stefano Ruffo
2019 arXiv   pre-print
The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can undergo first-order phase transitions. This is shown by studying a modified version of the Thirring model with attractive and repulsive interactions and with particles of finite size. The model exhibits first-order phase transitions in the unconstrained ensemble,
more » ... at variance with the analogous model with point-like particles. While unconstrained and grand canonical ensembles are equivalent for this model, we found inequivalence between the unconstrained and isothermal-isobaric ensembles. By comparing the thermodynamic phase diagram in the unconstrained case with that obtained in the isothermal-isobaric ensemble, we show that phase transitions under completely open conditions for this model are different from those in which the number of particles is fixed, highlighting the inequivalence of ensembles.
arXiv:1910.13997v1 fatcat:6jw2r2vxl5dwzni4bwb55y5uwi

Hydrodynamics and transport in the long-range-interacting φ^4 chain [article]

Stefano Iubini, Stefano Lepri, Stefano Ruffo
2022 arXiv   pre-print
We present a simulation study of the one-dimensional φ^4 lattice theory with long-range interactions decaying as an inverse power r^-(1+σ) of the intersite distance r, σ>0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0<σ≤ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and
more » ... s energy correlations shows that the effective hydrodynamics is diffusive for σ>1 and anomalous for 0<σ<1 where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.
arXiv:2112.02046v2 fatcat:ip7emlkj4remxouh4vp5b3m72i

Energetics of critical oscillators in active bacterial baths [article]

Ashwin Gopal, Édgar Roldán, Stefano Ruffo
2020 arXiv   pre-print
We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power ⟨Ẇ⟩∼ (D_ a/τ)^1/4 where D_ a is the effective diffusivity and τ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node
more » ... ion. Above the bifurcation, the average power attains an optimal, minimum value for finite τ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below 2k_ BT_ eff, with T_ eff the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.
arXiv:2011.00858v1 fatcat:ro4arvaxwbb7peruhdl47ujtve

Quantum-Heat Fluctuation Relations in Three-Level Systems Under Projective Measurements

Guido Giachetti, Stefano Gherardini, Andrea Trombettoni, Stefano Ruffo
2020 Condensed Matter  
We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for N-level systems, with N > 2 . Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor β eff that formally
more » ... ys the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of β eff for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.
doi:10.3390/condmat5010017 fatcat:ext7hfux4vczxnh36vm7nabkge

Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains [article]

Thierry Dauxois, Stefano Ruffo, Alessandro Torcini
1998 arXiv   pre-print
approximately linear at high Figure 2 : The solid line corresponds to the marginal stability curve ε 0 , the dashed one to ε M = ε(ρ max ) and the symbols to the points analytically found by Poggi and Ruffo  ... 
arXiv:cond-mat/9803001v1 fatcat:75jhs3ulhngmhosyed37vyq22q

Concavity, Response Functions and Replica Energy [article]

Alessandro Campa, Lapo Casetti, Ivan Latella, Agustín Pérez-Madrid, Stefano Ruffo
2018 Entropy   pre-print
In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated to the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are
more » ... d in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, physically meaningful only for nonadditive systems. In fact, its partition function is associated to the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.
doi:10.3390/e20120907 pmid:33266631 pmcid:PMC7512492 arXiv:1810.11309v1 fatcat:aug2t53atzdo5dhamdnbbr7vaa

Thermalization processes induced by quantum monitoring in multi-level systems [article]

Stefano Gherardini, Guido Giachetti, Stefano Ruffo, Andrea Trombettoni
2020 arXiv   pre-print
We study the heat statistics of an N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number of measurements. In this context, conditions allowing for Infinite-Temperature Thermalization (ITT), induced by the monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric
more » ... m matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the non-equilibrium evolution of the system and its initial state. Exceptions to ITT take place when the observable of the intermediate measurements is commuting (or quasi-commuting) with the Hamiltonian of the system, or when the time interval between measurements is smaller or comparable with the energy scale of the quantum system (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N →∞) - describing continuous systems with a discrete spectrum - are presented. By denoting with M the number of quantum measurements, we show that the order of the limits M →∞ and N →∞ matters: when N is fixed and M diverges, then there is ITT. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A non trivial result is obtained fixing M/N^2 where partial ITT occurs. Finally, an example of incomplete thermalization applicable to rotating two-dimensional gases is presented.
arXiv:2012.15216v1 fatcat:stltlfxjh5hwlcxjblmpltbnt4

Controversy about the applicability of Tsallis statistics to the HMF model [article]

Freddy Bouchet, Stefano Ruffo
2006 arXiv   pre-print
Comment to "Nonextensive Thermodynamics and Glassy Behaviour in Hamiltonian Systems" by A. Rapisarda and A. Pluchino, Europhysics News 36, 202 (2005).
arXiv:cond-mat/0605445v1 fatcat:2f4zd2b665ep3pa4iq4hxddtaa

Excitation of travelling multibreathers in anharmonic chains

Ramaz Khomeriki, Stefano Lepri, Stefano Ruffo
2002 Physica D : Non-linear phenomena  
We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When omega is in the phonon band, the p-mode becomes modulationally unstable above a critical forcing, which we determine analytically in terms of the parameters of the system. For omega above the phonon band, the instability of the p-mode leads to the formation of a
more » ... travelling multibreather, that, in the low-amplitude limit could be described in terms of soliton solutions of a suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar mechanisms of instability could show up in easy-axis magnetic structures, that are governed by such NLS equations.
doi:10.1016/s0167-2789(02)00503-1 fatcat:rlblscve4ba3reaw6vpkayavxi

Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise [article]

Shamik Gupta, Alessandro Campa, Stefano Ruffo
2014 arXiv   accepted
We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium
more » ... rder phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.
arXiv:1309.0035v2 fatcat:fln73ppvnngt3aqzakjewzvpoy

Computation of microcanonical entropy at fixed magnetization without direct counting [article]

Alessandro Campa, Giacomo Gori, Vahan Hovhannisyan, Stefano Ruffo, Andrea Trombettoni
2021 arXiv   pre-print
We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover, we apply the method to an Ising model with mean-field, nearest-neighbour and
more » ... eighbour interactions, for which direct counting is not straightforward. For this model, we compare the solution obtained by our method with the one obtained from the formula for the entropy in terms of all correlation functions. This example shows that for general couplings our method is much more convenient than direct counting methods to compute the microcanonical entropy at fixed magnetization.
arXiv:2107.12742v1 fatcat:6zk3ka2uezeftjoqimbnqyr7li

WNP: A Novel Algorithm for Gene Products Annotation from Weighted Functional Networks

Alberto Magi, Lorenzo Tattini, Matteo Benelli, Betti Giusti, Rosanna Abbate, Stefano Ruffo, Stefano Boccaletti
2012 PLoS ONE  
Predicting the biological function of all the genes of an organism is one of the fundamental goals of computational system biology. In the last decade, high-throughput experimental methods for studying the functional interactions between gene products (GPs) have been combined with computational approaches based on Bayesian networks for data integration. The result of these computational approaches is an interaction network with weighted links representing connectivity likelihood between two
more » ... tionally related GPs. The weighted network generated by these computational approaches can be used to predict annotations for functionally uncharacterized GPs. Here we introduce Weighted Network Predictor (WNP), a novel algorithm for function prediction of biologically uncharacterized GPs. Tests conducted on simulated data show that WNP outperforms other 5 state-of-the-art methods in terms of both specificity and sensitivity and that it is able to better exploit and propagate the functional and topological information of the network. We apply our method to Saccharomyces cerevisiae yeast and Arabidopsis thaliana networks and we predict Gene Ontology function for about 500 and 10000 uncharacterized GPs respectively.
doi:10.1371/journal.pone.0038767 pmid:22761703 pmcid:PMC3386258 fatcat:heppdjtcbjablpctw4lzz3px3a

Kolmogorov Pathways from Integrability to Chaos and Beyond [chapter]

Roberto Livi, Stefano Ruffo, Dima Shepelyansky
2003 Lecture Notes in Physics  
Two limits of Newtonian mechanics were worked out by Kolmogorov. On one side it was shown that in a generic integrable Hamiltonian system, regular quasi-periodic motion persists when a small perturbation is applied. This result, known as Kolmogorov-Arnold-Moser (KAM) theorem, gives mathematical bounds for integrability and perturbations. On the other side it was proven that almost all numbers on the interval between zero and one are uncomputable, have positive Kolmogorov complexity and,
more » ... e, can be considered as random. In the case of nonlinear dynamics with exponential (i.e. Lyapunov) instability this randomnesss, hidden in the initial conditions, rapidly explodes with time, leading to unpredictable chaotic dynamics in a perfectly deterministic system. Fundamental mathematical theorems were obtained in these two limits, but the generic situation corresponds to the intermediate regime between them. This intermediate regime, which still lacks a rigorous description, has been mainly investigated by physicists with the help of theoretical estimates and numerical simulations. In this contribution we outline the main achievements in this area with reference to specific examples of both lowdimensional and high-dimensional dynamical systems. We shall also discuss the successes and limitations of numerical methods and the modern trends in physical applications, including quantum computations.
doi:10.1007/978-3-540-39668-0_1 fatcat:4u4agw2ue5apljqry2xoh4ani4
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