We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a bath at the temperature $T$ and is driven by an unbiased time-periodic force. In the asymptotic long time regime the particle operates as a Brownian motor exhibiting finite directed transport although no net biasing force acts on the system. Here we review and interpret in further detail recent own research on the peculiar transport behaviour for this setup. The main focus is put on those different emerging Brownian diffusion anomalies. Particularly, within the transient, time-dependent domain the particle is able to exhibit anomalous diffusive motion which eventually crosses over into normal diffusion only in the asymptotic long-time limit. In the latter limit this normal diffusion coefficient may even show a non-monotonic temperature dependence, meaning that it is not monotonically increasing with increasing temperature, but may exhibit instead an extended, intermediate minimum before growing again with increasing temperature.
The density distributions and Soret coefficient in a nonequilibrium colloidal system with nonuniform temperature are studied by the overdamped Langevin equation for Brownian motion in an inhomogeneous strong friction medium. Based on the relation between the temperature gradient, the interaction potential and the q-parameter in nonextensive statistics, We show that the colloidal particle density can be a function of the temperature and anomalously follows the noted alpha-distribution, or equivalently it can also be a function of the potential energy and follows Tsallis distribution. With the q…
We investigate the size scaling of the entanglement entropy (EE) in nonequilibrium steady states (NESSs) of a one-dimensional open quantum system with a random potential. It models a mesoscopic conductor, composed of a long quantum wire (QWR) with impurities and two electron reservoirs at zero temperature. The EE at equilibrium obeys the logarithmic law. However, in NESSs far from equilibrium the EE grows anomalously fast, obeying the `quasi volume law,' although the conductor is driven by the zero-temperature reservoirs. This anomalous behavior arises from both the far from equilibrium condit…
We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating the first four current cumulants in a nonequilibrium stationary state at high energies, we find that the first two cumulants scale with the system size in a diffusive way, while the 3rd and the 4th cumulants do not. This means that the model is not an ordinary diffusive spin conductor.
We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-size lattices and show that a series of new critical exponents are needed to account for the anomalous scalings originating from breaking of self-similarity of the so-called phases fluctuations. Our results demonstrate that new exponents are generally required for scaling in the whole driven process once the lattice size or an externally applied field are taken into account. These open a new door in critical phenomena and suggest that much is yet to be explored in driven…
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With reference to a few models of classical coupled anharmonic oscillators, we review anomalous but general properties such as extremely slow relaxation processes, or non-Fourier heat transport.
Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry and appears ubiquitously in nature, a fundamental question is whether self-similarity breaking makes sense or not. Here, by identifying the most important kind of critical fluctuations dubbed as phases fluctuations and comparing the consequences of having self-similarity with those of lacking self-similarity in the phases fluctuations, we show that self-similarity can indeed be broken with significant consequences at least in nonequilibrium situations. We find that the breaking of self-similar…
We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size $\sqr…
We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of …
In a quasi-one-dimensional system the particles remain ordered from left to right allowing the association of a volume element to the particle which on average resides there. Thus the properties of that single particle can give the local densities in the volume element. With reservoirs of different temperatures connected to each end of the system a steady heat current with an anomalous thermal conductivity results. A local configurational entropy density is calculated from two-particle correlation functions which varies locally within the nonequilibrium steady state. This local configurational…
The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time $τ$ appears linearly, unless the process considered has long-range correlations, in which case $τ$ is generally replaced by $τ^ξ$ with $ξ\neq 1$. Here we show that such an anomalous power-law scaling in time of large deviations…
It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry, nonequilibrium topological phases of matter can exist in aperiodically driven systems for tunably parametrically long prethermal lifetimes. As a prerequisite, we first demonstrate the existence of longlived prethermal Anderson localization in two dimensions under random multipolar driving. We then show that the localization may be topologically nontrivial with a qu…
We complement and extend our work on fluctuation relations arising in nonequilibrium systems in steady states driven by Lévy noise [Phys. Rev. E 76, 020101(R) (2006)]. As a concrete example, we consider a particle subjected to a drag force and a Lévy white noise with tail index $μ\in (0,2]$, and calculate the probability distribution of the work done on the particle by the drag force, as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state. For $0<μ<2$, both distributions satisfy what we call an anomalous fluctuation relation, cha…
We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper critical dimension below which anomalous fluctuation driven scaling appears is d_c=6, in contrast to a widespread belief (see Dickman cond-mat 0110043 for an overview). We provide th…
We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of long-term correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator range increases, the surface develops a pattern of macroscopic facets that completely dominate the dynamics and induce anomalous kinetic roughening. This novel phenomenon is not described by the conventional dynamic renormalisation group calculations and can explain the singular behavior observed in the analytical treatment of this problem in the seminal paper of Medina {\…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the antisymmetry of spatial flux and the symmetry of velocity flux. Then we show that the condition of time-reversibility alone could not always guarantee the Maxwell-Boltzmann distribution. Comparing the two conditions together, we found that the frictional force naturally emerges as the unique odd term of the total force at thermodynamic equilibrium, and is followed by…
We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchet-like transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained resorting to a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation we explore the whole ordered phase finding a transition from anomalou…
In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $κ\propto L^α$. However, the exponent $α$ deviates systematically from the theoretical prediction $α=1/3$ proposed in a recen…
Molecular dynamics simulations and nonequilibrium importance sampling are used to study the heat transport of low dimensional carbon lattices. For both carbon nanotubes and graphene sheets heat transport is found to be anomalous, violating Fourier's law of conduction with a system size dependent thermal conductivity and concomitant nonlinear temperature profiles. For carbon nanotubes, the thermal conductivity is found to increase as the square root of the length of the nanotube, while for graphene sheets the thermal conductivity is found to increase as the logarithm of the length of the sheet.…
We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition, and particles diffusing in a anisotropic random advective field. It is exemplified how renormalisation group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We …
There is a growing interest in the stochastic processes of nonequilibrium systems subject to non-conserved forces, such as the magnetic forces acting on charged particles and the chiral self-propelled force acting on active particles. In this paper, we consider the stationary transport of non-interacting Brownian particles under a constant magnetic field in a position-dependent temperature background. We demonstrate the existence of the Nernst-like stationary density current perpendicular to both the temperature gradient and magnetic field, induced by the intricate coupling between the non-con…
A system of periodically coupled nonlinear phase oscillators submitted to both additive and multiplicative white noises has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis. These features stem from the "asymmetry" of the stationary probability distribution function, arising through a noise-induced nonequilibrium phase transition which is "reentrant" as a function of the multiplicative noise intensity. Using an explicit mean-field approximation we analyze the effect of the multiplicative noises being coloured, finding a contraction …
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second law like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.
Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{\langle x \rangle}_E)^2 ρ_E(x,t)dx \propto t^β$, as induced by a small initial excess energy perturbation distribution $ρ_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2C_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $ dMSD/dt|_{t=t_s} = 2/(k_BT^2c)\int_0^{t_s} C_{JJ}(s)ds$, where the chosen…
We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the probability distributions of mechanical and thermodynamical work in two paradigmatic nonequilibrium situations, respectively: a particle subject to a constant force and a particle in a harmonic potential dragged by a constant force. We check the transient FR for two models exhibiting superdiffusion, where a fluctuation-dissipation relation does not e…
It is experimentally known that virus exhibits stochastic motion in cytoplasm of a living cell in the free form as well as the form being contained in the endosome and the exponent of anomalous diffusion of the virus fluctuates depending on localized areas of the cytoplasm. Here, a theory is developed for establishing a generalized fractional kinetics for the infection pathway of the virus in the cytoplasm in view of superstatistics, which offers a general framework for describing nonequilibrium complex systems with two largely separated time scales. In the present theory, the existence of a l…
Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{< x >}_E)^2 ρ_E(x,t)dx \propto t^β$, as induced by a small initial excess energy perturbation distribution $ρ_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2C_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $ dMSD/dt|_{t=t_s} = 2/(k_BT^2c)\int_0^{t_s} C_{JJ}(s)ds$, where the chosen cut-off tim…
The spin 1/2 XXZ chain driven out of equilibrium by coupling with boundary reservoirs targeting perpendicular spin orientations in XY plane, is investigated. The existence of an anomaly in the nonequilibrium steady state (NESS) at the isotropic point $Δ=1$ is demonstrated both in the weak coupling and weak driving limits. The nature of the anomaly is studied analytically by calculating exact NESS for small system sizes, and investigating steady currents. The spin current at the points $Δ=\pm1$ has a singularity which leads to a current discontinuity when either driving or coupling vanish, and …
We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clea…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning valleys (hill tops) develop spontaneously and the surface facets for all growth (evaporation) biases. More intriguingly, the scaling properties of the rough one dimensional equilibrium surface are anomalous. Its width, $W\sim L^α$, diverges with system size $L$, as $α={1/3}$ instead of the conventional universal value $α={1/2}$. This originates from a topological…
We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where one or more of the inertial time scale(s), the memory time scale(s) and the noise correlation time scale(s) of the systems are taken to zero. We find that, unless one restricts to special situations that do not break symmetry of the Onsager matrix associated with the fast dynamics, it is generally not possible to express the effective evolution of these fun…
On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. Lévy on-off intermittency is a recently introduced generalisation of on-off intermittency to multiplicative Lévy noise, which depends on a stability parameter $α$ and a skewness parameter $β$. Here, we derive two novel results on Lévy on-off intermittency by leveraging known exact results on the first-passage time statistics of Lévy flights. First, we compute anomalous critical exponents…
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the non-equilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the time-scale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR …
A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a non-trivial interfacial region where the kinetic temperature is finite. Dynamics in such supercritical state displays anomalous chaotic properties whereby some observables are non-extensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the tem…
We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the random-force-driven one-dimensional Burgers' equation - a model for hydrodynamic turbulence. For a self-similar forcing acting on all scales the system is driven to a nonequilibrium steady state characterized by a Kolmogorov energy spectrum. We extract correlation functions of single- and multi-poin…
