Friction, reversibility, fluctuations in nonequilibrium

Different non-equilibrium ensembles can be used to model the same physical system: as in equilibrium different ensembles describe the same system. This will be illustrated in the case of the Lorenz96 model: a model governed by an irreversible chaotic dynamics which is shown to be equally well described by a similar model with reversible dynamics. A correspondence can be defined between the stationary states of the two models and corresponding states show the same statistical propertied, including the Lyapunov exponents. Scaling laws for the Lyapunov exponents, their pairing properties are obtained and the fluctuation relation is shown to hold (in the reversible model) confirming the chaotic hypothesis. (Joint work with V. Lucarini)

Energy spreading in strongly nonlinear lattices

We address the problem of the spreading of initially localized wave packet in disordered strongly nonlinear lattices. Using a nonlinear diffusion equation as a phenomenological model, we check scaling properties of the spreading in one and two dimension.

Equilibrium correlations and heat conduction in the Fermi-Pasta-Ulam chain.

Simulation results on various equilibrium spatio-temporal correlation functions in the Fermi-Pasta-Ulam chain will be presented. These are compared with the predictions of a recent theory of fluctuating hydrodynamics of anharmonic chains. A comparison between these equilibrium studies, and nonequilibrium studies measuring the thermal conductivity, will also be made and some of the puzzles will be discussed.

Dynamics of Ising spin systems

Two facets will be discussed: i) The interplay between reversibility and Gibbsianity, ii) A glimpse at the dynamics

Finite size effects in a mean-field kinetically constrained model: dynamical glassiness

On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics takes place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition – an argued signature of dynamical heterogeneities – to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. Results shed light on anomalous features of distributions of history-dependent observables in models of glasses.

Non Equilibrium Markov processes conditioned on large deviations

I will present a work done with Hugo Touchette (Phys Rev Lett 111, 120601, 2013). In this work, we consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the equivalent or driven process. The basic assumption is that the rare event used in the conditioning is a large-deviation-type event characterized by a convex rate function.

Physical ageing in non-equilibrium statistical systems without detailed balance

Since Struiks ground-breaking experiments on reproducible and universal properties of physical ageing glasses, many different spontaneously occurring relaxations in numerous many-body systems far from equilibrium have been systematically investigated. A compact way of characterising ageing systems is through the simultaneous properties of (i) slow relaxation, (ii) breaking of time-translation-invariance and (iii)dynamical scaling. Recent work has also furnished examples of the ageing phenomenology when the underlying microscopic dynamics is such that the stationary states are no longer equilibrium states. Since dynamical scaling is a recognised central ingredient to physical ageing, it appears natural to investigate on possible extensions to larger dynamical groups of time-space symmetries, in principle for generic values of the dynamical exponent z. Unexpected lessons from this approach concern the presence of several independent scaling dimensions of non-equilibrium scaling operators, the importance of the independent requirement of a suitable generalisation of Galilei-invariance and questions concerning the causality of co-variant n-point functions.

Current fluctuations in non equilibrium systems

The talk will review some results obtained over the last ten years on the fluctuations and the large deviations of the current in diffusive systems. In the steady state situation, (open system in contact with two reservoirs, ring geometry) the distribution of these fluctuations can be fully computed by the macroscopic fluctuation theory. For diffusive systems in non stationary situations, or mechanical systems the problem is much harder. A simple model where the transport is due to random walkers with Levy distributed fly times seems to reproduce some of the results in this unsolved cases.

Hydrodynamic limit and large deviations for a model of interacting self propelled particles

Joint work with: R. Chétrite, M. Muratori and F. Peruani Deriving hydrodynamic macroscopic equations from microscopic models of interacting self propelled particles is currently a very lively research field. One challenge is to take into account finite size fluctuations and understand their influence on macroscopic properties. We will show how this is possible to achieve in a model including alignment promoting interactions as well as density dependent velocities. However, the method works only in the locally disordered phase; when local order emerges, the macroscopic description is hyperbolic and new difficulties appear.

Non equilibrium free energies in systems with long range interactions and models of geophysical turbulence

The results discussed in this talks involve several works that have been done in collaborations with K.Gawedzki and C. Nardini (long range interactions), and J. Laurie, E. Simonnet, T. Tangarife, and O. Zaboronski (geostrophic turbulence).We will discuss the explicit computation of large deviation rate function in systems with a large number of degrees of freedom, for non-equilibrium dynamics (without detailed balance). We will first consider the dynamics of N particles integracting with two-body mean field potential and driven by anon equilibrium driving forces. The non-equilibrium free energies for empirical densities will be obtained as the quasi-potential in a Freidlin--Wentzell type low noise limit. In order to get explicit formulas for the quasi-potential, we will develop a general perturbative theory building on three key ingredients: i) the natural gradient structure for particle dynamics forced by white noise, (Otto-Villani), ii) the equivalence between transverse decomposition of vector fields, action minimization and solution of Hamilton-Jacobi equation (Jona Lasinio and collaborators), iii) perturbative technics.We will discuss similar approaches, aimed at computing explicitely non-equilibrium free energies, for models of geostrophic turbulence. For these models, non perturbative regimes will be considered. The dynamics then shows non-equilibrium phase transitions. A theory based on stochasticaveraging, and on two-time scale large deviations (Kiefer), will be discussed.

Experimental test of the connection between Jarzynski quality and the Landauer\'s bound

Rolf Landauer argued that the erasure of information is a dissipative process. A minimal quantity of heat, proportional to the thermal energy, is necessarily produced when a classical bit of information is deleted. A direct consequence of this logically irreversible transformation is that the entropy of the environment increases unavoidably by a finite amount. We experimentally show the existence of the Landauer bound in a generic model of a one-bit memory. Using a system of a single colloidal particle trapped in a modulated double-well potential, we establish that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles. This result demonstrates the intimate link between information theory and thermodynamics. For a memory erasure procedure, which is a logically irreversible operation, a detailed Jarzynski Equality is verified, retrieving the Landauer limit independently of the work done on the system.

Adventures of a long-range walker

In this talk, I will present recent results on systems with long-range interactions. Equilibrium and out-of-equilibrium properties will be discussed using several toy models. However, we will also consider realistic situations where long-range forces matter.

Einstein on the Boltzmann principle

Einstein calls the relationship between entropy and probability in equilibrium \'the Boltzmann principle\'. However he is skeptical about the possibility of determining microscopically the probability of a macroscopic state and looks for a phenomenological definition. He takes Boltzmann relationship as a definition of probability of an equilibrium state via thermodynamics and illustrates his point with arguments that in modern language we would call of large deviations. All this appears clearly in an unpublished talk at the Zurich Physical Society in 1910 and in a paper in the Annalen der Physik of the same year. This attitude reminds of his special relativity article where the empirical impossibility of observing absolute motion is taken as a principle and not as a fact to be explained, reversing in this way the prevailing views of the time. I will illustrate Einstein views on Boltzmann, their methodological implications and connections with recent work on non equilibrium.

Mixed order phase transitions

Phase transitions of mixed nature, which on the one hand exhibit a diverging correlation length as in second order transitions and on the other hand display a discontinuous order parameter as in first order transitions have been observed in a diverse classes of physical systems. Examples include models of wetting, glass and jamming transitions, DNA denaturation, rewiring networks  and some one-dimensional models with long-range interactions. An exactly soluble Ising model which provides a link between some of these rather distinct classes of systems is introduced. Renormalization group analysis which provides a common framework for studying some of these systems, elucidating the relation between them will be discussed. A. Bar and D. Mukamel, PRL 112, 015701 (2014)

Large and very large deviations in disordered systems

In disordered systems usually the free energy density does not fluctuate in the infinite volume limit when we extract the Hamiltonian of a system from a given probability distribution. However large deviations are possible. In this talk I will study the properties of the large deviation function in the mean field framework, where precise computations are possible. I will concentrate the attention on the study of the ground state energy using the replica approach. I will discuss the issue of large and very large deviation in a very simple case, the REM (the words “very large deviation” denote the case where the probability goes to zero faster than the exponential of the volume). Later on I will discuss more complex models: infinite coordination models (like the p=2 spherical model and the Sherrington Kirkpatrick model) and finite coordination models, like those on Bethe lattices.

A boundary-induced transition in chains of coupled oscillators

Chains of nonlinear oscillators are shown to exhibit a synchronization-like transition,when suitable forces are applied to the boundaries. This, zero-temperature, non-equilibrium phase transition induces two synchronized phases, separated by a non-trivial interfacial region, where the kinetic temperature is finite. The dynamics of the supercritical state is rather nontrivial: it corresponds to a mixture of extensive and non-extensive properties, the latter ones corresponding to an anomalous scaling with the system size (see, e.g., the width of the interfacial region).At finite temperatures, the transition is smoothed out, but it still induces peculiar properties such as a non-monotonous temperature-profile in the presence of equal-temperature heat baths. The scenario is observed both in the Hamiltonian XY model and the discrete nonlinear Schroedinger equation.

Nonlinear response theory in long-range Hamiltonian systems

The linear response theory has been developed recently for long-range Hamiltonian systems based on the Vlasov equation. However, the linear response theory does not work at the critical point of a second order phase transition, since the linear response diverges. To solve this problem, we propose a nonlinear response theory, and demonstrate how the theory works to compute the critical exponent.

Dynamics of a tagged monomer of a Rouse polymer: Effects of elastic pinning and harmonic absorption

A spatially extended system often involves a large number of degrees of freedom that are strongly interacting with one another. Correlations between different parts of the system may result in rather interesting static and dynamical properties that are both of theoretical and experimental relevance. As a case study, we analyze the dynamics of a tagged monomer of a Rouse polymer immersed in a solvent, for different initial configurations of the polymer. In the case of free evolution, the monomer displays subdiffusive behavior with strong memory of the initial state. In presence of either elastic pinning or harmonic absorption, our exact solution shows that the steady state is independent of the initial condition that however strongly affects the transient regime, resulting in non-monotonous behavior and power-law relaxation with varying exponents. Ref: SG, A. Rosso and C. Texier, Phys. Rev. Lett. 111, 210601 (2013)

Reaction Spreading on Graphs and Percolating Clusters

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, ds, for reaction spreading the important quantity is found to be the connectivity dimension, dl. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t) ~ td_l. In the case of Erdos-Renyi random graphs, the reaction-product is characterized by an exponential growth M(t) ~ ea t with a proportional to ln, where is the average degree of the graph. In addition in the case of two-dimensional percolating structures the front propagation through a percolating channel has been investigated.

Clausius\' Entropy Revisited

It is shown, that the equilibrium entropy, when a system in thermal equilibrium changes into a non-equilibrium system by appropriate external forces, transmutes into the organization of the currents in the non-equilibrium state, not into the entropy production in that state.

Universal current fluctuations in non equilibrium systems

We will show that the large deviations of the current in diffusive systems in contact with reservoirs have a universal structure which does not depend on the dimension, on the geometry of the domain or on the location of the reservoirs.

Fluctuation theorems in systems in contact with several baths: theory and experiments

I will first consider a harmonic chain coupled to two or more heat baths at different temperatures.I will use this model to introduce and discuss the fluctuation theorem that sets precise constraints on the fluctuations of the heat transfer between the different reservoirs.I will generalize these results to the case of systems with general interaction potential. I will then show some experimental results for a system formally equivalent to a harmonic chain with different heath baths, and show that a conservation law for the total entropy exists. Finally, I will discuss the general case of a system in contact with multiple energy and particle baths, and show that there exists a fluctuation theorem that involves only the energy and the particle currents and that holds at any time. References H. C. Fogedby, A. Imparato, Heat flow in driven chains,J. Stat. Mech. P04005 (2012). S. Ciliberto, A. Imparato, A. Naert, M. Tanase, On the heat flux and entropy produced by thermal fluctuations, Phys. Rev. Lett., 110: 180601 (2013).S. Ciliberto, A. Imparato, A. Naert, M. Tanase, Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations, J. Stat. Mech. P12014 (2013).G. Bulnes Cuetara, M. Esposito, A. Imparato, Exact fluctuation theorem without ensemble quantities, arXiv:1402.1873

Kondo-signature in heat transfer via local two-state system

We study the Kondo effect in heat transport via a local two-states system. This system is described by the spin-boson Hamiltonian with Ohmic dissipation, which can be mapped onto the (electric) Kondo model with anisotropic exchange coupling. We calculate thermal conductance by the Monte Carlo method based on the exact formula. Thermal conductance has a scaling form. Temperature dependence of conductance is classified by the Kondo temperature. Similarities to the Kondo signature in electric transport are discussed.Ref.: Phys.Rev.Lett. vol.111, 214301 (2013)

Dynamical spin properties in helical Luttinger liquids

An overview of spin dynamical properties in helical edges states will be presented. Spin textures and crystallization phenomena in helical topological insulators and in spin Hall quantum dots will be discussed [1,2]. Particular attention will be devoted to the effects induced by electron correlations and by the spin-momentum locking, hallmark of these systems. [1] G. Dolcetto, F. Cavaliere, M. Sassetti, Phys. Rev. B 89, 125419 (2014). [2] G. Dolcetto, N. Traverso Ziani, M. Biggio, F. Cavaliere, M. Sassetti, Phys. Rev. B 87, 235423 (2013).

Rare events and scaling in superdiffusive materials and in field-induced anomalous dynamics

Large fluctuations and rare events play an important role in many physical processes, where heterogeneous spatial structures or temporal inhomogeneities can give rise to anomalous transport. We consider here two effects, driven by rare events, in transport processes. On Levy walks and continuous time random walks with broad waiting times distribution, we study the effects of an arbitrary small external field and show that this can induce an anomalous growth of fluctuations, even when the unperturbed behavior is Gaussian. We then consider transport on a class of random structures with Levy-like disorder, where correlations between long steps arise. We characterize the superdiffusive behavior by a \"single-long-jump approximation\", that allows to estimate the effects of rare events.

Geometry-Induced Superdiffusion in Driven Crowded Systems

The classical experiment of micro-rheology consists of tracking the motion of a colloidal particle, due to thermal fluctuations or in the presence of an external  constant force, to learn the properties of the surrounding fluid. We consider the Simple Exclusion Process (SEP) and model microrheology as one Asymmetric SEP in a sea of Symmetric SEP\'s. Using First-Passage Time techniques, we obtain exact asymptotic expressions for the probability distribution function of the ASEP\'s displacement in arbitrary dimensions. For dimensions greater or equal than 3 the ASEP\'s dynamics is diffusive. In lower dimensions the dynamics become super diffusive. Our results can be clearly explained in terms of the lattice\'s mixing properties and are naturally extended to off-lattice dynamics in terms of the Wiener sausage of Brownian motion.

Statistical Mechanics of Self-Gravitating Systems

Systems with long-range forces behave very differently from those in which particles interact through short-range potentials [1]. Unlike short-range interacting systems, in thermodynamic limit long-range systems do not relax to the usual thermodynamic equilibrium, but become trapped in quasi stationary states (QSS), the life time of which diverges with the number of particles. In this talk we will discuss the relaxation to QSS of one, two, and three dimensional self-gravitating systems. We will show that if the initial particle distribution satisfies the virial condition, it is possible to very accurately predict the final QSS in any dimension. On the other hand if the initial distribution does not satisfy the virial condition, strong density oscillation will result in parametric resonances which, for 3d systems, can lead to particle evaporation. This makes it very difficult to a priori predict he particle distribution inside a QSS in 3d, for initially non-virial distributions. In one and two dimensions, the unbounded form of Newton’s gravitational potential prevents particles from escaping to infinity. For these dimensions we will present a theory which allows us to a priori calculate the particle distribution inside QSS [2,3] which arise for initially non-virial distributions. Finally, we will show that if the initial condition is sufficiently far from virial, a spherical symmetry of the initial distribution can become spontaneously broken. We will present a theory which can be used to establish the stability threshold for the spontaneous symmetry breaking for two and three dimensional self-gravitating systems [4]. [1] Y. Levin, R. Pakter, F. B. Rizzato, T. N. Telles, F. P. C. Benetti, Phys. Rep. 535, 1 (2014). [2] T. N. Teles, Y. Levin, and R. Pakter, Mon. Not. R. Astron. Soc. 417, L21 (2011). [3] T.N. Teles, Y.Levin, R. Pakter, and F.B. Rizzato, J. Stat. Mech. P05007 (2010). [4] R. Pakter, B. Marcos, and Y. Levin, Phys. Rev. Lett. 111, 230603 (2013).

Nonequilibrium statistical mechanics of electrons in a diode

A statistical theory is presented that allows the calculation of the stationary state achieved by the electron flow in a diode after a process of collisionless relaxation. The stationary Vlasov equation with appropriate boundary conditions is reduced to an ordinary differential equation, which is then solved numerically. Special attention is given to the space-charge limited transition when the electron density becomes high enough to screen the accelerating electric field at the cathode. It is found that while for unmagnetized diodes this transition is always continuous, in the case of crossed-field diodes it becomes discontinuous below a critical temperature. We also investigate how intrinsic space-charge oscillations may drive stationary states unstable in certain parameter regimes. The results are verified with molecular-dynamics simulations.

Nonequilibrium dynamics of long-range lattice models

Long-range interactions between the constituents of a many-body system can lead to unconventional behaviour in- as well as out-of-equilibrium. In this talk I present results on the non-equilibrium dynamics of classical and quantum long-range lattice systems, focussing on peculiarities like supersonic propagation in the absence of a finite group velocity, infinite separation of time scales, prethermalisation, and others. Various experimental realisations are discussed and measurements in ion trap-based long-range quantum simulators are reviewed.

Theory for a realistic model for fish schools

We will present a realistic model for fish schools reproducing swarming (fishes move erratically), schooling (fishes have a common average velocity), and milling (a \"vortex\"-like phase), which has been introduced and validated experimentally by Guy Theraulaz\' group at CRCA. We will present analytic results for the one-fish dynamics including the interaction with the tank wall, and the two-fish dynamics. Moreover, we will present a mean-field treatment of the model for a large number of fishes, and its phase diagram. The strong analogy (but also the differences) with the Hamiltonian Mean-Field (HMF) model, a paradigm for long range interacting systems, will be emphasized.

Adaptation as a nonequilibrium paradigm

The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the strength of extracellular stimulus. The working principles of adaptation have been established previously based on rate equations which do not consider fluctuations in a thermal environment. Recently, G. Lan et al. (Nature Phys., 8:422-8, 2012) performed a detailed analysis of a stochastic model for the E. coli sensory network. They showed that accurate adaptation is possible only when the system operates in a nonequilibrium steady-state. They further obtained a relation among energy dissipation, adaptation speed and adaptation error through model calculation and suggested that it may hold generally. However, adaptation is only one aspect of the bacterial chemo-sensing system.Its transient response to ligand concentration fluctuations with high gain is at least as important. We present here a more refined calculation on the system’s response at all frequencies. The simplicity of the model allows a rigorous treatment using methods of statistical mechanics. The model also possesses several desirable analytic properties which make it an attractive testing ground to demystify various general results on energy dissipation and linear response in nonequilibrium states, including for example the Harada-Sasa equality for a discrete-state Markov system.

From phase to micro-phase separation in Flocking Models

I will present an active Ising model in which spins both diffuse and align on lattice in one and two dimensions. The diffusion is biased so that plus or minus spins hop preferably to the left or to the right, which generates a flocking transition at low temperature/high density. Using a coarse-grained description of the model, I will show this transition to amount to a first-order liquid-gas transition in the canonical ensemble, with a critical density sent to infinity. I will then show how this scenario evolves when the discrete symmetry of the model is replaced by a continuous symmetry, as in the Vicsek model. In particular, I will show that in the coexistence region, one observes micro-phase rather than phase-separation. This can only be understood at a fluctuating hydrodynamic level.

Spatial extent of an outbreak in animal epidemics

Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, and therefore, fluctuations around their average are important: then, it is commonly assumed that the susceptible–infected–recovered mechanism can be described by a stochastic birth–death process of Galton–Watson type. The displacements of the infected individuals can be modeled by resorting to Brownian motion, which is applicable when long-range movements and complex network interactions can be safely neglected, like in the case of animal epidemics. In this context, the spatial extent of an epidemic can be assessed by computing the convex hull enclosing the infected individuals at a given time. We derive the exact evolution equations for the mean perimeter and the mean area of the convex hull, and we compare them with Monte Carlo simulations.

Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators

When the energy content of a resonant mode of a crystalline solid in thermodynamic equilibrium is measured, it coincides with temperature except for a proportionality factor. This is due to the principle of energy equipartition, which does not hold, in general, away from thermodynamic equilibrium. We address the question of how violations of equipartition take place in specific cases, and what is common to different cases. We report on experimental and numerical tests on low-frequency modes of vibration of certain solid bars subjected to heat fluxes. We illustrate the strong dependence on the heat flux of the energy associated with low-frequency normal modes, and we provide a theoretical explanation, which agrees quantitatively with the observations, based on flux-mediated correlations between non-equilibrium modes.

To what extent are the mechanical features of a small system relevant to its thermostatistical behaviour?

The law of heat conduction, i.e., the property by which the heat flux density is equal to the product of the conductance by minus the temperature difference emerges as a paradigmatic manifestation of the laws of thermodynamics. Despite of the fact that anomalies were already found in the 1960s, the problem of heat conduction has kept on being regarded as purely thermodynamic. Inspired by a wide range of non-linear (small) systems, which span from surface diffusion and low vibrational motion with adsorbates to biological motors, wherein the energy source is the stochastic hydrolysis of adenosine triphosphate (ATP), we will theoretically discuss to what extend the heat conduction is a simple manifestation of the physics of a system in contact with reservoirs at different temperatures, independently of their natures. In addition, we will introduce predictions about whether or not the mechanical features of the system can influence thermodynamical measurements in experiments and its impact on the universality of the laws of thermodynamics.

Aging of Classical Oscillators during a Noise-Driven Migration of Oscillators Phases

Physical aging is a familiar phenomenon from glassy systems like spin glasses and materials. It is characterized by slow relaxation processes, breaking of time-translation invariance, and dynamical scaling. We study aging in active rotators and Kuramoto oscillators that are coupled with frustrated bonds. The induced multiplicity of attractors of fixed-point or limit-cycle solutions leads to a rough potential landscape. In combination with the lattice symmetry and periodic boundary conditions the attractor diversity can become particularly rich. When the system is exposed to noise, the oscillator phases migrate through this landscape and generate a multitude of different escape times from one metastable state to the next. When the system is quenched from the regime of a unique collective fixed point towards a regime of multistable limit-cycle solutions, the autocorrelation functions depend on the waiting time after the quench and show dynamical scaling. In this way we uncover a common mechanism behind aging in quite different realizations. References: P. Kaluza and H. Meyer-Ortmanns, Chaos 20, 043111 (2010). F. Ionita, D. Labavic, M. Zaks and H. Meyer-Ortmanns, Eur. Phys. J. B 86, 511 (2013). F. Ionita and H. Meyer-Ortmanns, Physical Aging of Classical Oscillators, Phys. Rev. Lett. 112, 094101 (2014).

Everlasting initial memory threshold for rare events in equilibration processes

Conventional wisdom indicates that initial memory should decay away exponentially in time for general (non critical) equilibration processes. In particular, time-integrated quantities such as heat are presumed to lose initial memory in a sufficiently long-time limit. However, we show that the large deviation function of time-integrated quantities may exhibit initial memory effect even in the infinite-time limit, if the system is initially prepared sufficiently far away from equilibrium. For a Brownian particle dynamics, as an example, we found a sharp finite threshold rigorously, beyond which the corresponding large deviation function contains everlasting initial memory. The physical origin for this phenomenon is explored with an intuitive argument and also from a toy model analysis. Our results can be applied to general non-equilibrium relaxation processes reaching (non)equilibrium steady states

Propagating fronts and random matrix spectra in the XX spin chain

Relaxation starting from step-like transverse magnetization profile in the XX spin chain is considered. It is found that the propagating fronts emerging from such an initial state display a staircase structure that can be interpreted in terms of particles moving with a finite velocity and spreading subdiffusively. We determine the probability distribution of the number of particles at the edge of the front exactly and find that the full counting statistics is described by the edge spectrum of matrices from the Gaussian unitary ensemble. The correspondence between particle positions and the eigenvalues also allows the calculation of the extreme order statistics of the particles and, furthermore, it also explains their subdiffusive spreading.

First passage fluctuation relations ruled by cycle affinities

or a non-equilibrium stationary state that can be described by stochastic thermodynamics it is well-known that the entropy production rate can be expressed in terms of the affinity associated with every transition bond in the graph representation of the master equation. Affinity along cycles in the latter graph are shown to obey a first passage fluctuation relation which gives a natural probabilistic interpretation of these cycle affinities. Contrarily to seminal fluctuation relations about the probability for the entropy produced during a given time, the latter fluctuation relation deals with the probability for the time needed for one cycle to be performed in one sense or in the opposite one. Reference : M. Bauer and F. Cornu, J. Stat. Phys., 155 (2014) 703-736

Validity of spin wave theory for the quantum Heisenberg model

We consider the quantum Heisenberg ferromagnet in three dimensions. We present the first rigorous proof of validity of the spin-wave approximation at low temperatures, at the level of the system\'sfree energy. The proof combines a bosonic formulation of the model induced by the Holstein-Primakoff representation with probabilistic estimates,localization bounds and functional inequalities. Joint work with Michele Correggi and Robert Seiringer.

Adaptive networks with preferred degree: from the mundane to the surprising

Network studies have played a central role for understanding many systems in nature - e.g., physical, biological, and social. So far, much of the focus has been static networks in isolation. Yet, many networks are dynamic, coupled to each other. We considered this issue, in the context of social networks. In particular, We introduce a simple model of adaptive networks, modeling a society in which an individual cuts/adds links based on whether he or she has more/less links than some \"preferred number\" (kappa). For example, introverts/extroverts typically have small/large kappa\'s. Evolving with detailed balance violating dynamics, the steady state distribution of this dynamic network is not known in general, though it displays reasonably understandable properties. After a brief summary of systems with a single kappa and one with two groups with different kappa\'s, I will present the details of a system with \"extreme introverts (I) and extroverts (E)\" (kappa = 0 and infinity). With just two control parameters (i.e., the numbers of I\'s and E\'s), this system displays an extraordinary transition, much like those recently studied by Mukamel and collaborators (e.g., Bar and Mukamel, PRL 112, 015701 (2014)). Beyond this theoretically interesting limit of our system, we outline some potentially important applications, such as modeling the response to a spreading epidemic by a population with adaptive behavior.

The Kac model coupled with a thermostat.

We study a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse temperature β. The system admits the canonical distribution at inverse temperature β as the unique equilibrium state. We derive the rate at which the system tends to equilibrium, both, in the sense of the spactral gap and in the sense of relative entropy. This is joint work with Michael Loss and Ranjini Vaidyanathan.

3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise

We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4. This confirms some recent predictions of Spohn based on the nonlinear fluctuating hydrodynamics theory.

Universal record statistics of random walks.

I will present recent exact results which we have obtained for the statistics of records of a correlated time series generated by the positions of a random walker (RW) after N time steps. I will focus on the number of records R_N as well as on the ages of the longest and shortest lasting records, whose statistics can be computed exactly using first passage techniques. In particular, I will show how universality emerges from the Sparre Andersen theorem. I will also discuss further extensions to the case of RW with a drift as well as generalizations to records of multi-particle systems.

A class of exactly solved assisted-hopping models of active-absorbing state transition on a line

We construct a class of assisted hopping models in one dimension in which a particle can move only if it has exactly one occupied neighbour, or if it lies in an otherwise empty interval of length le=n+1. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density ρ of particles, from a low-density phase with all particles immobile for ρ<ρc=1/(n+1), to an active state for ρ>ρc The mean fraction of movable particles in the active steady state varies as (ρ-ρc)β, for ρ near ρc. We show that for the model with range n, the exponent β=n, and thus can be made arbitrarily large.

New concepts emerging from a linear response theory for nonequilibrium

The fluctuation-dissipation theorem states that the natural fluctuations in an equilibrium system are proportional to its response to external perturbations, which takes place via a dissipation, or entropy production. Generalized relations show that this is not the case out of equilibrium: in general, the response may be seen as a the sum of two terms, one resembling the equilibrium form, and one related to a less studied time-symmetric aspect of the dynamics. We discuss the role of this second term, also in relation with the notion of dynamical activity, which was recently introduced to characterize the evolution of systems with kinetically constrained dynamics. The generalized relations help to understand responses not as intuitive as those in equilibrium (negative differential mobility, etc.) and may be formulated also for perturbations in a bath temperature rather than in external forces.

Information thermodynamics of a feedback control for cold damping

We investigate a feedback control for cold damping where the measurement outcome of a particle\\\'s momentum is applied as a protocol for friction. We use the theory of information thermodynamics for the process composed of measurement, information (memory) acquisition, computation (post-measurement by feedback) that has been inspired by the paradox of Maxwell\\\'s demon. We extend the feedback theory to a measurement of odd-parity variable such as momentum. We consider the feedback process in multiple steps and investigate the efficiency for cold damping depending on the time interval between measurements and time delay of feedback.

Anomalous chaotic atomic transport in optical lattices

A semiclassical theory of chaotic anomalous atomic transport in a one-dimensional nondissipative optical lattice, when the standing-wave field and center-of-mass motion are treated classically, is developed. Using the basic equations of motion for the Bloch and translational atomic variables, we derive a stochastic map for the synchronized component of the atomic dipole moment that determines the center-of-mass motion. We find the analytical relations between the atomic and lattice parameters under which atoms typically alternate between flying through the lattice and being trapped in the wells of the optical potential. We use the stochastic map to derive formulas for the probability density functions (PDFs) for the flight and trapping events. Statistical properties of chaotic atomic transport strongly depend on the relations between the atomic and lattice parameters. We show that there is a good quantitative agreement between the analytical PDFs and those computed with the stochastic map and the basic equations of motion for different ranges of the parameters. Typical flight and trapping PDFs are shown to be broad distributions with power law segments with the slope $-1.5$ and exponential tails\'\'. The lengths of the power law and exponential segments of the PDFs depend on the values of the parameters. We find analytical conditions under which deterministic atomic transport has fractal properties and explain a hierarchical structure of the dynamical fractals.