arXiv subjects

Michel Pleimling

Publications and source records attributed to Michel Pleimling.

At least 73 records · Page 4Linked to original sources

arXiv2011

The Jarzynski Identity and the AdS/CFT Duality

We point out a remarkable analogy between the Jarzynski identity from non-equilibrium statistical physics and the AdS/CFT duality. We apply the logic that leads to the Jarzynski identity to renormalization group (RG) flows of quantum field theories and then argue for the natural connection with the AdS/CFT duality formula. This application can be in principle checked in Monte Carlo simulations of RG flows. Given the existing generalizations of the Jarzynski identity in non-equilibrium statistical physics, and the analogy between the Jarzynski identity and the AdS/CFT duality, we are led to suggest natural but novel generalizations of the AdS/CFT dictionary.

hep-th↗

arXiv2011

Realm of Validity of the Crooks Relation

We consider the distribution $P(ϕ)$ of the Hatano-Sasa entropy, $ϕ$, in reversible and irreversible processes, finding that the Crooks relation for the ratio of the pdf's of the forward and backward processes, $P_F(ϕ)/P_R(-ϕ)=e^ϕ$, is satisfied not only for reversible, but also for irreversible processes, in general, in the adiabatic limit of "slow processes." Focusing on systems with a finite set of discrete states (and no absorbing states), we observe that two-state systems always fulfill detailed balance, and obey Crooks relation. We also identify a wide class of systems, with more than two states, that can be "coarse-grained" into two-state systems and obey Crooks relation despite their irreversibility and violation of detailed balance. We verify these results in selected cases numerically.

cond-mat.stat-mech↗

arXiv2011

Nonequilibrium phase transition in a driven Potts model with friction

We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state which is far from equilibrium. The problem is treated analytically in the limit $v=\infty$ (in one dimension, as well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.

cond-mat.stat-mech↗

arXiv2011

Entropy production in the non-equilibrium steady states of interacting many-body systems

Entropy production is one of the most important characteristics of non-equilibrium steady states. We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of non-equilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing non-equilibrium steady states of interacting many-body systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

cond-mat.stat-mech↗

arXiv2010

Cyclic competition of four species: mean field theory and stochastic evolution

Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous model, the four form alliance pairs which resemble partnership in the game of Bridge. In a finite system with discrete stochastic dynamics, all but 4 of the absorbing states consist of coexistence of a partner-pair. From a master equation, we derive a set of mean field equations of evolution. This approach predicts complex time dependence of the system and that the surviving partner-pair is the one with the larger product of their strengths (rates of consumption). Simulations typically confirm these scenarios. Beyond that, much richer behavior is revealed, including complicated extinction probabilities and non-trivial distributions of the population ratio in the surviving pair. These discoveries naturally raise a number of intriguing questions, which in turn suggests a variety of future avenues of research, especially for more realistic models of multispecies competition in nature.

q-bio.PE↗

arXiv2010

Aging in coarsening diluted ferromagnets

We comprehensively study non-equilibrium relaxation and aging processes in the two-dimensional random-site Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various two-times quantities as a function of temperature and of the degree of dilution. For already modest values of the dynamical correlation length $L$ deviations from a simple algebraic growth, $L(t) \sim t^{1/z}$, are observed. When taking this non-algebraic growth properly into account, a simple aging behavior of the autocorrelation function is found. This is in stark contrast to earlier studies where, based on the assumption of algebraic growth, a superaging scenario was postulated for the autocorrelation function in disordered ferromagnets. We also study the scaling behavior of the space-time correlation as well as of the time integrated linear response and find again agreement with simple aging. Finally, we briefly discuss the possibility of superuniversality in the scaling properties of space- and time-dependent quantities.

cond-mat.stat-mech↗

arXiv2010

Nonequilibrium relaxation and scaling properties of the two-dimensional Coulomb glass in the aging regime

We employ Monte Carlo simulations to investigate the two-time density autocorrelation function for the two-dimensional Coulomb glass. We find that the nonequilibrium relaxation properties of this highly correlated disordered system can be described by a full aging scaling ansatz. The scaling exponents are non-universal, and depend on temperature and charge density.

cond-mat.stat-mech↗

arXiv2010

Characterisation of non-equilibrium growth through global two-time quantities

In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions and show that the scaling behaviour of the global response can depend on how the system is perturbed. On the one hand we derive exact expressions for systems characterised by linear Langevin equations (as for example the Edwards-Wilkinson and the noisy Mullins-Herring equations), on the other hand we discuss the influence of non-linearities on the scaling behaviour of global quantities by integrating numerically the Kardar-Parisi-Zhang equation. We also discuss global fluctuation-dissipation ratios and how to use them for the characterisation of non-equilibrium growth processes.

cond-mat.stat-mech↗

arXiv2010

Convection cells induced by spontaneous symmetry breaking

Ubiquitous in nature, convection cells are a clear signature of systems out-of-equilibrium. Typically, they are driven by external forces, like gravity (in combination with temperature gradients) or shear. In this article, we show the existence of such cells in possibly the simplest system, one that involves only a temperature gradient. In particular, we consider an Ising lattice gas on a square lattice, in contact with two thermal reservoirs, one at infinite temperature and another at $T$. When this system settles into a non-equilibrium stationary state, many interesting phenomena exist. One of these is the emergence of convection cells, driven by spontaneous symmetry breaking when $T$ is set below the critical temperature.

cond-mat.stat-mech↗

arXiv2010

Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here discuss rock-paper-scissors games on a one-dimensional lattice where the interaction rates and the mobility can be species dependent. Allowing only single site occupation, we realize mobility by exchanging individuals of different species. When the interaction and swapping rates are symmetric, a strongly enhanced swapping rate yields an increased mixing of the species, leading to a mean-field like coexistence even in one-dimensional systems. This coexistence is transient when the rates are asymmetric, and eventually only one species will survive. Interestingly, in our spatial games the dominating species can differ from the species that would dominate in the corresponding nonspatial model. We identify different regimes in the parameter space and construct the corresponding dynamical phase diagram.

q-bio.PE↗

arXiv2009

Changing growth conditions during surface growth

Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters. We discuss quenches between correlated regimes through exact expressions derived from the stochastic Edwards-Wilkinson equation with a variable diffusion constant. Our study reveals that a sudden change of the diffusion constant leads to remarkable changes in the surface roughness. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We conclude that growth processes provide one of the rare instances where quenches between correlated regimes yield a power-law relaxation.

cond-mat.stat-mech↗

arXiv2009

Non-markovian global persistence in phase-ordering kinetics

The persistence probability P_g(t) of the global order-parameter of a simple ferromagnet undergoing phase-ordering kinetics after a quench from a fully disordered state to below the critical temperature, T<T_c, is analysed. It is argued that the persistence probability decays algebraically with time in the entire low-temperature phase. For Markov processes, the associated global persistence exponent theta_g = (2 lambda_C -d)/(2z) is related to the autocorrelation exponent lambda_C. This relationship is confirmed for phase-ordering in the exactly solved 1D Ising model and the d-dimensional spherical model. For the 2D Glauber-Ising model, theta_g=0.063(2) is found which indicates that the dynamics of the global order-parameter is described by a non-markovian process.

cond-mat.stat-mech↗

arXiv2009

Characterizing steady state and transient properties of reaction-diffusion systems

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions both in their steady states and out of stationarity. Many reaction-diffusion systems have the peculiarity that microscopic reversibility is broken such that their transient behavior can not be investigated through the study of most of the observables discussed in the literature. For this reason we analyze the transient properties of reaction-diffusion systems through a specific work observable that remains well defined even in the absence of microscopic reversibility and that obeys an exact detailed fluctuation relation in cases where detailed balance is fulfilled. We thereby drive the systems out of their nonequilibrium steady states through time-dependent reaction rates. Using a numerical exact method and computer simulations, we analyze fluctuation ratios of the probability distributions obtained during the forward and reversed processes. We show that the underlying microscopic dynamics gives rise to peculiarities in the configuration space trajectories, thereby yielding prominent features in the fluctuation ratios.

cond-mat.stat-mech↗

arXiv2009

Microcanonical phase diagrams of short-range ferromagnets

A phase diagram is a graph in parameter space showing the phase boundaries of a many-particle system. Commonly, the control parameters are chosen to be those of the (generalized) canonical ensemble, such as temperature and magnetic field. However, depending on the physical situation of interest, the (generalized) microcanonical ensemble may be more appropriate, with the corresponding control parameters being energy and magnetization. We show that the phase diagram on this parameter space looks remarkably different from the canonical one. The general features of such a microcanonical phase diagram are investigated by studying two models of ferromagnets with short-range interactions. The physical consequences of the findings are discussed, including possible applications to nuclear fragmentation, adatoms on surfaces, and cold atoms in optical lattices.

cond-mat.stat-mech↗

arXiv2009

Parameter free scaling relation for nonequilibrium growth processes

We discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this new scaling relation through various growth models, as for example the competitive growth model RD/RDSR (random deposition/random deposition with surface diffusion) and the RSOS (restricted solid-on-solid) model with different nearest-neighbor height differences, as well as through a new deposition model with temperature dependent diffusion. The new scaling relation is compared to the familiar Family-Vicsek relation and the limitations of the latter are highlighted.

cond-mat.stat-mech↗

arXiv2009

Fluctuation Ratios in the Absence of Microscopic Time Reversibility

We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic time reversibility. Studying a quantity that for an equilibrium system is related to the work done to the system, we observe that under certain conditions oscillations appear on top of an exponential behavior of transient fluctuation ratios. We argue that these oscillations encode properties of the probability currents in state space.

cond-mat.stat-mech↗

arXiv2009

Superuniversality in phase-ordering disordered ferromagnets

The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform bond disorder is investigated by intensive Monte Carlo simulations. Simple ageing behaviour is observed in the single-time correlator and the two-time responses and correlators. The dynamical exponent z and the autocorrelation exponent lambda_C only depend on the ratio eps/T, where eps describes the width of the distribution of the disorder, whereas a more complicated behaviour is found for the non-equilibrium exponent a of the two-time response as well as for the autoresponse exponent lambda_R. The scaling functions are observed to depend only on the dimensionless ratio eps/T. If the length scales are measured in terms of the time-dependent domain size L(t), the form of the scaling functions is in general independent of both eps and T. Conditions limiting the validity of this `superuniversality' are discussed.

cond-mat.dis-nn↗

arXiv2008

Non-relativistic AdS/CFT and Aging/Gravity Duality

We point out that the recent discussion of non-relativistic AdS/CFT correspondence has a direct application in non-equilibrium statistical physics, the fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent $z=2$ and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

cond-mat.stat-mech↗