Entropy-driven phase transitions with influence of the field-dependent diffusion coefficient (original) (raw)
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Journal of Physical Studies
We present study concerns a generalization of the model for extended stochastic systems with a field-dependent kinetic coefficient and a noise source satisfying fluctuation-dissipation relation. Phase transitions with entropy driven mechanism are investigated in systems with conserved and nonconserved dynamics. It is found that in stochastic systems with a relaxational flow and a symmetric local potential reentrant phase transitions can be observed. We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems of reaction diffusion kind. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. Our mean-field results are verified by computer simulations.
Nonequilibrium fluctuations for linear diffusion dynamics
Physical Review E, 2011
We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function and (ii) diffusion matrix not proportional to the unit matrix, implying non-identical and correlated multi-dimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution P (W) in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get P (W). We find an interesting dynamic phase transition in the exponential tail shape of P (W), associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.
Nonequilibrium phase transitions induced by multiplicative noise
Physical Review E, 1997
We review a mean-field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise, white in space and time. We confirm the existence of a pure noise-induced reentrant nonequilibrium phase transition in the model introduced in ͓C. Van den Broeck et al., Phys. Rev. Lett. 73, 3395 ͑1994͔͒, give an intuitive explanation of its origin, and present extensive simulations in dimension dϭ2. The observed critical properties are compatible with those of the Ising universality class.
Nonequilibrium phase transitions induced by multiplicative noise: Effects of self-correlation
Physical Review E, 2000
We review a mean-field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise, white in space and time. We confirm the existence of a pure noise-induced reentrant nonequilibrium phase transition in the model introduced in ͓C. Van den Broeck et al., Phys. Rev. Lett. 73, 3395 ͑1994͔͒, give an intuitive explanation of its origin, and present extensive simulations in dimension dϭ2. The observed critical properties are compatible with those of the Ising universality class.
Role of fluctuations for inhomogeneous reaction-diffusion phenomena
Physical Review A, 1991
Although Auctuations have been known to change the long-time behavior of homogeneous diA'usionreaction phenomena dramatically in dimensions d~4, simulations of reaction fronts in two-dimensional 3 +8~C inhomogeneous systems have only shown marginal departure from mean-field behavior. We perform cellular-automata simulations of the one-dimensional case and find that the width 8 (t) of the reaction front behaves as t '-', in contrast to mean-field behavior t'. We develop a scaling theory to obtain inequalities for the exponents in the more general mechanism n 3+mB-+C. Heuristic arguments about the range of fluctuations imply that the mean-field behavior should be correct in dimensions larger than an upper critical dimension d"p =2, irrespective of the values of n and m. This leads us to reinterpret the two-dimensional data obtained previously in terms of a logarithmic correction to meanfield behavior.
Diffusion in systems with static disorder
Physical Review B, 1984
%'e study diffusion in systems with static disorder, characterized by random transition rates I w"), which may be assigned to the bonds [random-barrier model (RBM)] or to the sites [randomjump-rate model (RIM)]. We make an expansion in powers of the fluctuations 5"=(to"'-(w '))/ (w ') around the exact diffusion coefficient D=1/(to ') in the low frequency regime, using diagrammatic methods. For the one-dimensional models we obtain a systematic expansion in powers of Vz of the response function (transport properties) and Green's function (spectral properties}. The frequency-dependent diffusion coefficient in the RBM is found as Uo(z)=D-, a2V-Dz +cxoz+a)z + ' ', where K2= (5),cxo mcludes lip to fourth-order flllctuatlons and cx) lip to sixth order. In the RJM, Uo(z) =B. Similarly, we obtain results (very different in RBM and RJM) for the frequency-dependent Burnett coefficient Uq(z} and the single-site Green s function Go(z) [which determines the density of eigenstates M(e} and the inverse locaHzation length y(e} of relaxational modes of tlM system]. The spectral properties of both models are ideIltlcal Slid agree with exact results at low frequencies for the spectral properties of random harmonic chains. The long-time behauior of the velocity autocorrelation function in RBM is q& (t)=()t 'r~+(.)t '~' and for the Burnett correlation function p4(t)=(.~~)t ', with coefficients that vanish on a uniform lattice. For the RJM, g2(t)=&6+(t) and y4(t)=()t '~. The long-time behavior of the moments of displacement (n), and (n4), and the staying probability Po(t) are calculated up to relative order t~. A comparison of our exact results with those of the effective-medium (or hypernettedchain) approximation (EMA) shows that the coefficient ao in Uo(z) as given by EMA is incorrect, contlary to suggestions made ln the literature. For the RJM all results can be tlivially extended to higher-dimensional systems.
Noise-induced phase transition and the percolation problem for fluctuating media with diffusion
The diffusion problem is considered for a medium in which processes of disintegration and of reproduction of the diffusing substance are possible. The critical intensities of the fluctuations in the disintegration and reproduction rates, which lead to the occurrence of noise-induced explosive instability, are determined. The effects of suppression of such instability by nonlinear limitation mechanisms are analyzed. Fluctuation phenomena near the noise-induced phase-transition point are investigated. Sov. Phys. JETP 52(5), Nov. 1980 0038-5646/80/110989-08$02.40 O 1981 American Institute of Physics 989 995 Sov, Phys. JETP 52(5), NOV. 1980 A. S. ~ikhaylov and I. V. Uporov 995
Transitions from deterministic to stochastic diffusion
Europhysics Letters (epl), 2002
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding different types of time-dependent noise to this model we compute the diffusion coefficient from simulations. We find that there is a crossover from deterministic to stochastic diffusion under variation of the perturbation strength related to different asymptotic laws for the diffusion coefficient. Typical signatures of this scenario are suppression and enhancement of normal diffusion. Our results are explained by a simple theoretical approximation. PACS numbers: 05.60.Cd, 05.45.Ac, 05.40.Jc To understand diffusion in noisy maps, that is, in time-discrete dynamical systems where the deterministic equations of motion are perturbed by noise, figures as a prominent problem in recent literature. The most simple example of such models are one-dimensional chaotic maps on the line. In seminal contributions by Geisel and Nierwetberg [1], and by Reimann et al. [2], scaling laws have been derived for the diffusion coefficient yielding suppression and enhancement of diffusion with respect to variation of the noise strength. Related results have been obtained in Refs. . However, all these results apply only to the onset of diffusion where the scaling laws are reminiscent of a dynamical phase transition, and not much appears to be known far away from this transition point. In such more general situations, only perturbations by a nonzero average bias have been studied . Related models are deterministic Langevin equations, in which the interplay between deterministic and stochastic chaos has been analyzed [6], however, without focusing on diffusion coefficients. Non-diffusive noisy maps have furthermore been investigated by refinements of cycle expansion methods .
Phase transitions induced by noise cross-correlations
Physical Review E, 2005
A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective Fokker-Planck equation whose stationary solutions describe a character of ordered state. We find that fluctuation cross-correlations lead to a symmetry breaking of the distribution function even in the case of the zero-dimensional system. In general case, continuous, discontinuous and reentrant noise induced phase transitions take place. It is appeared the cross-correlations play a role of bias field which can induce a chain of phase transitions being different in nature. Within mean field approach, we give an intuitive explanation of the system behavior through an effective potential of thermodynamic type. This potential is written in the form of an expansion with coefficients defined by temperature, intensity of spatial coupling, autoand cross-correlation times and intensities of both additive and multiplicative noises.
Dynamical phase transitions in disordered systems: the study of a random walk model
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