Journal ArticleDOI
External non-white noise and nonequilibrium phase transitions
José M. Sancho,M. San Miguel +1 more
TLDR
In this article, Langevin equations with external non-white noise are considered and a Fokker Planck equation valid in general in first order of the correlation timeτ of the noise is derived.Abstract:
Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation timeτ of the noise is derived. In some cases its validity can be extended to any value ofτ. The effect of a finiteτ in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed.read more
Citations
More filters
Book
Extended irreversible thermodynamics
TL;DR: In this paper, the authors propose a theory which goes beyond the classical formulation of thermodynamics by enlarging the space of basic independent variables, through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations.
Book
Noise-induced transitions
TL;DR: In this article, the effect of external random perturbations, "noise", on chemical systems and other open nonlinear systems is studied. But the authors do not consider the effects of external noise on the dynamics of the system.
Journal ArticleDOI
REVIEW ARTICLE: Extended irreversible thermodynamics
Journal ArticleDOI
Path-integral formulation for stochastic processes driven by colored noise
TL;DR: In this paper, a detailed discussion of the path-integral formalism for stochastic processes described by a nonwhite noise is given, and the stationary distribution of the process in the weak noise limit is obtained from the Lagrangian without relying on the use of Fokker-Planck or Markovian approximations.
References
More filters
Journal ArticleDOI
Statistical Dynamics of Classical Systems
TL;DR: In this article, the statistical dynamics of a classical random variable that satisfies a nonlinear equation of motion is recast in terms of closed self-consistent equations in which only the observable correlations at pairs of points and the exact response to infinitesimal disturbances appear.
Book
Stochastic differential equations
TL;DR: In this article, the authors introduce the notion of a stochastic differential equation and prove general theorems concerning the existence and uniqueness of solutions of these equations, which is a generalization of the notions of integral integral integral functions.