Dynamical Widom-Rowlinson model and its mesoscopic limit
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy, Maria Joao, Oliveira
TL;DR
This paper studies the non-equilibrium dynamics of the Widom-Rowlinson model in the continuum, deriving kinetic equations and analyzing phase transitions and bifurcations in the mesoscopic limit.
Contribution
It introduces a Lebowitz-Penrose-type scaling for the dynamics and derives the associated kinetic equations for the Widom-Rowlinson model without hard-core.
Findings
Equilibrium points of the kinetic system are characterized.
The structure of equilibrium points indicates a dynamical phase transition.
Bifurcation analysis reveals critical points in the model's dynamics.
Abstract
We consider the non-equilibrium dynamics for the Widom-Rowlinson model (without hard-core) in the continuum. The Lebowitz-Penrose-type scaling of the dynamics is studied and the system of the corresponding kinetic equations is derived. In the space-homogeneous case, the equilibrium points of this system are described. Their structure corresponds to the dynamical phase transition in the model. The bifurcation of the system is shown.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Complex Systems and Time Series Analysis