We investigate the phase transitions in a coupled system of Ising spins and a fluctuating network. Each spin interacts with $q$ neighbors through links of the rewiring network. The Ising spins and the network are in thermal contact with the heat baths at temperatures $T_S$ and $T_L$, respectively, so that the whole system is driven out of equilibrium for $T_S \neq T_L$. The model is a generalization of the $q$-neighbor Ising model, which corresponds to the limiting case of $T_L=\infty$. Despite the mean field nature of the interaction, the $q$-neighbor Ising model was shown to display a discontinuous phase transition for $q\geq 4$. Setting up the rate equations for the magnetization and the energy density, we obtain the phase diagram in the $T_S$-$T_L$ parameter space. The phase diagram consists of a ferromagnetic phase and a paramagnetic phase. The two phases are separated by a continuous phase transition belonging to the mean field universality class or by a discontinuous phase transition with an intervening coexistence phase. The equilibrium system with $T_S=T_L$ falls into the former case while the $q$-neighbor Ising model falls into the latter case. At the tricritical point, the system exhibits the mean field tricritical behavior. Our model demonstrates a possibility that a continuous phase transition turns into a discontinuous transition by a nonequilibrium driving. Heat flow induced by the temperature difference between two heat baths is also studied.
We show the existence of a nonequilibrium tricritical point induced by a repulsive interaction in one dimensional asymmetric exclusion process. The tricritical point is associated with the particle-hole symmetry breaking introduced by the repulsion. The phase diagram and the crossover in the neighbourhood of the tricritical point for the shock formation at one of the boundaries are determined.
The dynamic phase transition has been studied in the two dimensional kinetic Ising model in presence of a time varying (sinusoidal) magnetic field by Monte Carlo simulation. The nature (continuous or discontinuous) of the transition is characterized by studying the distribution of the order parameter and the temperature variation of the fourth order cumulant. For the higher values of the field amplitude, the transition observed is discontinuous and it is continuous for lower values of the field amplitude, indicating the existence of a tricritical point (separating the nature of the transition)…
We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which corr…
We demonstrate that first-order phase transitions in 1+1-dimensional nonequilibrium systems with fluctuating ordered phases are impossible, provided that there are no additional conservation laws, long-range interactions, macroscopic currents, or special boundary conditions. Since minority islands in the ordered phase of such systems can only shrink by short-range interactions, it is impossible to stabilize a fluctuating ordered state. The apparent first-order behavior turns out to be a transient phenomenon, crossing over to a continuous transition after very long time. As examples we consider…
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and velocity in the single-particle phase space. The symmetry relation concerns the fluctuating particle and energy currents of the gas flowing between reservoirs or thermalizing surfaces at given particle densities or temperatures.
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of tempo…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled through the sine of their phase differences. We study here a variation of the model by including nearest-neighbor interactions on a one-dimensional lattice. While the mean-field interaction resulting from the global coupling favors global synchrony, the nearest-neighbor interaction may have cooperative or competitive effects depending on the sign and the magnitud…
The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system.
We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in s-states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to d-states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here, we consider a quantum spin model…
We introduce a simple continuous model for nonequilibrium surface growth. The dynamics of the system is defined by the KPZ equation with a Morse-like potential representing a short range interaction between the surface and the substrate. The mean field solution displays a non trivial phase diagram with a first order transition between a growing and a bound surface, associated with a region of coexisting phases, and a tricritical point where the transition becomes second order. Numerical simulations in 3 dimensions show quantitative agreement with mean field results, and the features of the pha…
A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occu…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational states of these biological macromolecules. A recently developed theoretical framework [Wachtel, Vollmer, Altaner: "Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics"] provides a simple algorithm for the determination of macroscopic currents and correlation integrals of arbitrary fluctuating currents. Here, we use it to…
We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave-packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in ti…
The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition becomes discontinuous. As the diffusion probability increases the critical exponents change continuously from the ordinary directed percolation (DP) class to the compact directed percolation (CDP). The fractal dimension of the critical cluster, however, switches abruptly between those two universality classes. Strong crossover effects in both methods make it dif…
We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle density and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow…
Systems coupled to multiple thermodynamic reservoirs can exhibit nonequilibrium dynamics, breaking detailed balance to generate currents. To power these currents, the entropy of the reservoirs increases. The rate of entropy production, or dissipation, is a measure of the statistical irreversibility of the nonequilibrium process. By measuring this irreversibility in several biological systems, recent experiments have detected that particular systems are not in equilibrium. Here we discuss three strategies to replace binary classification (equilibrium versus nonequilibrium) with a quantification…
We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size $N$, the probability of any macroscopic density profile $ρ(x)$ is $\exp[-N{\cal F}(\{ρ\})]$; ${\cal F}$ thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for $\cal F$ is a nonlocal functional of $ρ$, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experi…
We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.
We extend our earlier macrostatistical treatment of hydrodynamical fluctuations about nonequilibrium steady states to viscous fluids. Since the scale dependence of the Navier-Stokes equations precludes the applicability of any infinite scale (hydrodynamical) limit, this has to be based on the generic model of a large but finite system, rather than an infinite one. On this basis, together with assumptions of Onsager's regression hypothesis and conditions of local equilibrium and chaoticity, we show that the hydrodynamical fluctuations of a reservoir driven fluid about a nonequilibrium steady st…
A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large class of nonequilibrium systems. For such a manifestly nonlinear nonequilibrium strongly fluctuating system, we show that there exists universal nonequilibrium critical behavior that is well described incredibly by its equilibrium critical properties. A dynamic renormalization-group theory is developed to account for the behavior. The weak driving may give ris…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed.…
We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase, separated by a critical line. We present an analytical study of the nonequilibrium properties of the fluctuating number of balls in a given urn, considering successively the temporal evolution of its distribution, of its two-time correlation and response functions, and of the associated \fd ratio, both along the critical line and in the condensed phase. For …
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g. in the channel system of some zeolites or in artificial optical lattices. In our model involving two species of particles a steady-state particle current is maintained by a density gradient between the channel boundaries and by the influence of an external driving force. This leads to the development of a fluctuating but always microscopically sharp interfac…
We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel generalizations of the second law of thermodynamics and the fluctuation theorem, which include an informational quantity characterized by the topology of the causal network. Our result implies that the entropy production in a single system in the presence of multiple other systems is bounded by the information flow between these systems. We demonstrate our general re…
We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in different ways. As a result of this two-way coupling between the landscape and the particles, the system shows interesting new phases, characterized by different sorts of long ranged order in the particles and in the landscape. In all these ordered phases the two particle species phase separate completely from each other, but the underlying landscape may either sho…
Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a new, physically transparent derivation of a metric tensor for which the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibrium optimization problems by recasting them in a geometric…
Recent advances in experimental techniques allow one to measure and control systems at the level of single molecules and atoms. Here gaining information about fluctuating thermodynamic quantities is crucial for understanding nonequilibrium thermodynamic behavior of small systems. To achieve this aim, stochastic thermodynamics offers a theoretical framework, and nonequilibrium equalities such as Jarzynski equality and fluctuation theorems provide key information about the fluctuating thermodynamic quantities. We review the recent progress in quantum fluctuation theorems, including the studies o…
Vesicles, or closed fluctuating membranes, have been modeled in two dimensions by self-avoiding polygons, weighted with respect to their perimeter and enclosed area, with the simplest model given by area-weighted excursions. These models generically show a tricritical phase transition between an inflated and a crumpled phase, with a scaling function given by the logarithmic derivative of the Airy function. Extending such a model, we find realizations of multicritical points of arbitrary order, with the associated multivariate scaling functions expressible in terms of generalized Airy integrals…
We derive the fluctuation dynamics of a probe in weak coupling with a "living" medium, modeled as particles undergoing an active Ornstein-Uhlenbeck dynamics. Nondissipative corrections to the fluctuation-dissipation relation are written out explicitly in terms of time-correlations in the active medium. A first term changes the inertial mass of the probe, as a consequence of the persistence of the active medium. A second correction modifies the friction kernel. The resulting generalized Langevin equation benchmarks the motion induced on probes immersed in active versus passive media. The deriva…
Nonequilibrium phase transition properties of the $\pm J$ Ising model under a time dependent oscillating perturbation are investigated within the framework of effective field theory for a two-dimensional square lattice. After a detailed analysis, it is found that the studied system exhibits unusual and interesting behaviors such as reentrant phenomena, and the competition between ferromagnetic and antiferromagnetic exchange interactions gives rise to destruct the dynamic first order phase transitions as well as dynamic tricritical points. Furthermore, according to Néel nomenclature, the magnet…
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population causes a dense bacterial colony to form, which then declines by local cell death, before dispersing to re-initiate the cycle. Adding fluctuations, we find that static colonies are now metastable, moving between spatial locations via rare and strongly nonequilibrium pathways, whereas the limit cycle becomes almost periodic such that after each redispersion event…
We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-d…
We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the …
Effects of strongly anisotropic turbulent mixing on the critical behavior are studied by means of the renormalization group. Two models are considered: the equilibrium model A, which describes purely relaxational dynamics of a nonconserved scalar order parameter, and the Gribov model, which describes the nonequilibrium phase transition between the absorbing and fluctuating states in a reaction-diffusion system. The velocity is modelled by the d-dimensional generalization of the random shear flow introduced by Avellaneda and Majda within the context of passive scalar advection. Existence of new…
Within the framework of unified approach we study the Casimir-Lifshitz interaction, the van der Waals friction force and the radiative heat transfer at nonequilibrium conditions, when the interacting bodies are at different temperatures, and they move relative to each other with the arbitrary velocity $V$. The analysis is focused on the surface-surface and surface-particle configuration. Our approach is based on the exact solution of electromagnetic problem about the determination of the fluctuating electromagnetic field in the vacuum gap between two flat parallel surfaces moving relative to e…
Superstatistics is a `statistics of a statistics' relevant for driven nonequilibrium systems with fluctuating intensive parameters. It contains Tsallis statistics as a special case. We show that the probability density functions of velocity differences and accelerations measured in Eulerian and Lagrangian turbulence experiments are well reproduced by simple superstatistics models. We compare fits obtained for log-normal superstatistics and chi-squared superstatistics (= Tsallis statistics).
Beyond local detailed balance: Microscopic rates reshape nonequilibrium phase behavior
The University of Tokyo（东京大学）；RIKEN Pioneering Research Institute（理化学研究所先锋研究本部）；Department of Physics, The University of Chicago（芝加哥大学物理系）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理学研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所跨学科理论与数学科学中心）；RIKEN Center for Biosystems Dynamics Research（理化学研究所生物系统动力学研究中心）
The $q$-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their $q$ neighbors. Depending on the model parameters in Monte Carlo simulations phase diagrams are observed with first-order ferromagmetic transit…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary/ecological dynamics of competing bacterial populations. Range expansion -- the stochastic reproduction of bacteria competing for space to be occupied by their progeny -- leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP tr…
