On the macroscopic nonequilibrium dynamics of an exclusion process

2005 ◽  
pp. 225-239
Author(s):  
E. Platen
Keyword(s):  
Exclusion Process ◽  
Nonequilibrium Dynamics

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

Self-organization based on nonlinear nonequilibrium. Dynamics of autonomous agents

1998 ◽  
Vol 2 (3) ◽  
pp. 102-107 ◽  
Author(s):  
S. Kurihara ◽  
T. Sugawara ◽  
R. Onai
Keyword(s):  
Autonomous Agents ◽  
Self Organization ◽  
Nonequilibrium Dynamics

scholarly journals Nonequilibrium Dynamics of Coupled Qubit-Cavity Arrays

2012 ◽  
Vol 108 (23) ◽  
Author(s):  
Felix Nissen ◽  
Sebastian Schmidt ◽  
Matteo Biondi ◽  
Gianni Blatter ◽  
Hakan E. Türeci ◽  
...  
Keyword(s):  
Nonequilibrium Dynamics

Coarse-Grain Model Simulations of Nonequilibrium Dynamics in Heterogeneous Materials

2014 ◽  
Vol 5 (12) ◽  
pp. 2144-2149 ◽  
Author(s):  
John K. Brennan ◽  
Martin Lísal ◽  
Joshua D. Moore ◽  
Sergei Izvekov ◽  
Igor V. Schweigert ◽  
...  
Keyword(s):  
Heterogeneous Materials ◽  
Nonequilibrium Dynamics ◽  
Coarse Grain ◽  
Model Simulations ◽  
Grain Model
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